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1.

図書
図書
1. Introduction to analysis on graphs
Alexander Grigor'yan
出版情報: Providence, R.I. : American Mathematical Society, c2018  viii, 150 p. ; 26 cm
シリーズ名: University lecture series ; v. 71
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2.

図書
図書
2. Graphs and discrete Dirichlet spaces
Matthias Keller, Daniel Lenz, Radosław K. Wojciechowski
出版情報: Cham : Springer, c2021  xv, 668 p. ; 25 cm
シリーズ名: Die Grundlehren der mathematischen Wissenschaften ; v. 358
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3.

図書
図書
3. Elementary number theory, group theory, and Ramanujan graphs (: hb ; : pbk)
Giuliana Davidoff, Peter Sarnak, Alain Valette
出版情報: Cambridge : Cambridge University Press, 2003  viii, 144 p. ; 24 cm
シリーズ名: London Mathematical Society student texts ; 55
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目次情報: 続きを見る
An overview
Graph theory / 1：
Number theory / 2：
PSL2(q) / 3：
The graphs Xp, q / 4：
4-regular graphs with large girth / Appendix A：
Index
Bibliography
An overview
Graph theory / 1：
Number theory / 2：
4.

図書
図書
4. Algorithms, graphs, and computers
Richard Bellman, Kenneth L. Cooke, Jo Ann Lockett
出版情報: New York : Academic Press, 1970  xv, 246 p. ; 24 cm
シリーズ名: Mathematics in science and engineering : a series of monographs and textbooks ; v. 62
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5.

図書
図書
5. Combinatorial configurations, designs, codes, graphs (: usa ; : uk)
Vladimir D. Tonchev ; translated from the Bulgarian by Robert A. Melter
出版情報: Harlow, Essex, England : Longman Scientific & Technical , New York : Copublished in the U.S. with John Wiley, 1988  189 p. ; 24 cm
シリーズ名: Pitman monographs and surveys in pure and applied mathematics ; 40
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6.

図書
図書
6. Spectra of graphs : theory and application
Dragoš M. Cvetković, Michael Doob, Horst Sachs
出版情報: New York ; London : Academic Press, c1979  368 p. ; 24 cm
シリーズ名: Pure and applied mathematics ; 87
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目次情報: 続きを見る
Introduction
Basic Concepts of the Spectrum of a Graph
Operations on Graphs and the Resulting Spectra
Relations Between Spectral and Structural Properties of Graphs
The Divisor of a Graph
The Spectrum and the Group of Automorphisms
Characterization of Graphs by Means of Spectra
Spectra Techniques in Graph Theory and Combinatories
Applications in Chemistry an Physics
Some Additional Results
Appendix
Tables of Graph Spectra Biblgraphy
Index of Symbols
Index of Names
Subject Index
Introduction
Basic Concepts of the Spectrum of a Graph
Operations on Graphs and the Resulting Spectra
7.

図書
図書
7. Graph algorithms (: us ; : uk ; : gw)
Shimon Even
出版情報: Potomac, Md. : Computer Science Press, c1979  ix, 249 p. ; 24 cm
シリーズ名: Computer software engineering series
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8.

図書
図書
8. Graphs, models, and finite mathematics
Joseph Malkevitch, Walter Meyer
出版情報: Englewood Cliffs, N.J. : Prentice-Hall, c1974  x, 515 p. ; 24 cm
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9.

図書
図書
9. Graphs, groups, and surfaces. Completely rev. and enl. ed (: pbk)
Arthur T. White
出版情報: Amsterdam ; New York : North-Holland , New York, N.Y., U.S.A. : Sole distributors for the U.S.A. and Canada, Elsevier Science Pub. Co., 1984  xiii, 314 p. ; 24 cm
シリーズ名: North-Holland mathematics studies ; 8
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10.

図書
図書
10. Graphs and networks (: pbk)
Bernard Carré
出版情報: Oxford : Clarendon Press , New York : Oxford University Press, 1979  xvi, 277 p. ; 23 cm
シリーズ名: Oxford applied mathematics and computing science series
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11.

図書
図書
11. Topological graph theory
Jonathan L. Gross, Thomas W. Tucker
出版情報: New York : Wiley, c1987  xv, 351 p. ; 24 cm
シリーズ名: Wiley interscience series in discrete mathematics and optimization
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目次情報: 続きを見る
Introduction / 1.：
Representation of graphs / 1.1.：
Drawings / 1.1.1.：
Incidence matrix / 1.1.2.：
Euler's theorem on valence sum / 1.1.3.：
Adjacency matrix / 1.1.4.：
Directions / 1.1.5.：
Graphs, maps, isomorphisms / 1.1.6.：
Automorphisms / 1.1.7.：
Exercises / 1.1.8.：
Some important classes of graphs / 1.2.：
Walks, paths, and cycles; connectedness / 1.2.1.：
Trees / 1.2.2.：
Complete graphs / 1.2.3.：
Cayley graphs / 1.2.4.：
Bipartite graphs / 1.2.5.：
Bouquets of circles / 1.2.6.：
New graphs from old / 1.2.7.：
Subgraphs / 1.3.1.：
Topological representations, subdivisions, graph homeomorphisms / 1.3.2.：
Cartesian products / 1.3.3.：
Edge-complements / 1.3.4.：
Suspensions / 1.3.5.：
Amalgamations / 1.3.6.：
Regular quotients / 1.3.7.：
Regular coverings / 1.3.8.：
Surfaces and imbeddings / 1.3.9.：
Orientable surfaces / 1.4.1.：
Nonorientable surfaces / 1.4.2.：
Imbeddings / 1.4.3.：
Euler's equation for the sphere / 1.4.4.：
Kuratowski's graphs / 1.4.5.：
Genus of surfaces and graphs / 1.4.6.：
The torus / 1.4.7.：
Duality / 1.4.8.：
More graph-theoretic background / 1.4.9.：
Traversability / 1.5.1.：
Factors / 1.5.2.：
Distance, neighborhoods / 1.5.3.：
Graphs colorings and map colorings / 1.5.4.：
Edge operations / 1.5.5.：
Algorithms / 1.5.6.：
Connectivity / 1.5.7.：
Planarity / 1.5.8.：
A nearly complete sketch of the proof / 1.6.1.：
Connectivity and region boundaries / 1.6.2.：
Edge contraction and connectivity / 1.6.3.：
Planarity theorems for 3-connected graphs / 1.6.4.：
Graphs that are not 3-connected / 1.6.5.：
Kuratowski graphs for higher genus / 1.6.6.：
Other planarity criteria / 1.6.8.：
Voltage Graphs and Covering Spaces / 1.6.9.：
Ordinary voltages / 2.1.：
Drawings of voltage graphs / 2.1.1.：
Fibers and the natural projection / 2.1.2.：
The net voltage on a walk / 2.1.3.：
Unique walk lifting / 2.1.4.：
Preimages of cycles / 2.1.5.：
Which graphs are derivable with ordinary voltages? / 2.1.6.：
The natural action of the voltage group / 2.2.1.：
Fixed-point free automorphisms / 2.2.2.：
Cayley graphs revisited / 2.2.3.：
Automorphism groups of graphs / 2.2.4.：
Irregular covering graphs / 2.2.5.：
Schreier graphs / 2.3.1.：
Relative voltages / 2.3.2.：
Combinatorial coverings / 2.3.3.：
Most regular graphs are Schreier graphs / 2.3.4.：
Permutation voltage graphs / 2.3.5.：
Constructing covering spaces with permutations / 2.4.1.：
Preimages of walks and cycles / 2.4.2.：
Which graphs are derivable by permutation voltages? / 2.4.3.：
Identifying relative voltages with permutation voltages / 2.4.4.：
Subgroups of the voltage group / 2.4.5.：
The fundamental semigroup of closed walks / 2.5.1.：
Counting components of ordinary derived graphs / 2.5.2.：
The fundamental group of a graph / 2.5.3.：
Contracting derived graphs onto Cayley graphs / 2.5.4.：
Surfaces and Graph Imbeddings / 2.5.5.：
Surfaces and simplicial complexes / 3.1.：
Geometric simplicial complexes / 3.1.1.：
Abstract simplicial complexes / 3.1.2.：
Triangulations / 3.1.3.：
Cellular imbeddings / 3.1.4.：
Representing surfaces by polygons / 3.1.5.：
Pseudosurfaces and block designs / 3.1.6.：
Orientations / 3.1.7.：
Stars, links, and local properties / 3.1.8.：
Band decompositions and graph imbeddings / 3.1.9.：
Band decomposition for surfaces / 3.2.1.：
Orientability / 3.2.2.：
Rotation systems / 3.2.3.：
Pure rotation systems and orientable surfaces / 3.2.4.：
Drawings of rotation systems / 3.2.5.：
Tracing faces / 3.2.6.：
Which 2-complexes are planar? / 3.2.7.：
The classification of surfaces / 3.2.9.：
Euler characteristic relative to an imbedded graph / 3.3.1.：
Invariance of Euler characteristic / 3.3.2.：
Edge-deletion surgery and edge sliding / 3.3.3.：
Completeness of the set of orientable models / 3.3.4.：
Completeness of the set of nonorientable models / 3.3.5.：
The imbedding distribution of a graph / 3.3.6.：
The absence of gaps in the genus range / 3.4.1.：
The absence of gaps in the crosscap range / 3.4.2.：
A genus-related upper bound on the crosscap number / 3.4.3.：
The genus and crosscap number of the complete graph K[subscript 7] / 3.4.4.：
Some graphs of crosscap number 1 but arbitarily large genus / 3.4.5.：
Maximum genus / 3.4.6.：
Distribution of genus and face sizes / 3.4.7.：
Algorithms and formulas for minimum imbeddings / 3.4.8.：
Rotation-system algorithms / 3.5.1.：
Genus of an amalgamation / 3.5.2.：
Crosscap number of an amalgamation / 3.5.3.：
The White-Pisanski imbedding of a cartesian product / 3.5.4.：
Genus and crosscap number of cartesian products / 3.5.5.：
Imbedded Voltage Graphs and Current Graphs / 3.5.6.：
The derived imbedding / 4.1.：
Lifting rotation systems / 4.1.1.：
Lifting faces / 4.1.2.：
The Kirchhoff Voltage Law / 4.1.3.：
Imbedded permutation voltage graphs / 4.1.4.：
An orientability test for derived surfaces / 4.1.5.：
Branched coverings of surfaces / 4.1.7.：
Riemann surfaces / 4.2.1.：
Extension of the natural covering projection / 4.2.2.：
Which branch coverings come from voltage graphs? / 4.2.3.：
The Riemann-Hurwitz equation / 4.2.4.：
Alexander's theorem / 4.2.5.：
Regular branched coverings and group actions / 4.2.6.：
Groups acting on surfaces / 4.3.1.：
Graph automorphisms and rotation systems / 4.3.2.：
Regular branched coverings and ordinary imbedded voltage graphs / 4.3.3.：
Which regular branched coverings come from voltage graphs? / 4.3.4.：
Applications to group actions on the surface S[subscript 2] / 4.3.5.：
Current graphs / 4.3.6.：
Ringel's generating rows for Heffter's schemes / 4.4.1.：
Gustin's combinatorial current graphs / 4.4.2.：
Orientable topological current graphs / 4.4.3.：
Faces of the derived graph / 4.4.4.：
Nonorientable current graphs / 4.4.5.：
Voltage-current duality / 4.4.6.：
Dual directions / 4.5.1.：
The voltage graph dual to a current graph / 4.5.2.：
The dual derived graph / 4.5.3.：
The genus of the complete bipartite graph K[subscript m, n] / 4.5.4.：
Map Colorings / 4.5.5.：
The Heawood upper bound / 5.1.：
Average valence / 5.1.1.：
Chromatically critical graphs / 5.1.2.：
The five-color theorem / 5.1.3.：
The complete-graph imbedding problem / 5.1.4.：
Triangulations of surfaces by complete graphs / 5.1.5.：
Quotients of complete-graph imbeddings and some variations / 5.1.6.：
A base imbedding for orientable case 7 / 5.2.1.：
Using a coil to assign voltages / 5.2.2.：
A current-graph perspective on case 7 / 5.2.3.：
Orientable case 4: doubling 1-factors / 5.2.4.：
About orientable cases 3 and 0 / 5.2.5.：
The regular nonorientable cases / 5.2.6.：
Some additional tactics / 5.3.1.：
Nonorientable cases 3 and 7 / 5.3.2.：
Nonorientable case 0 / 5.3.4.：
Nonorientable case 4 / 5.3.5.：
About nonorientable cases 1, 6, 9, and 10 / 5.3.6.：
Additional adjacencies for irregular cases / 5.3.7.：
Orientable case 5 / 5.4.1.：
Orientable case 10 / 5.4.2.：
About the other orientable cases / 5.4.3.：
Nonorientable case 5 / 5.4.4.：
About nonorientable cases 11, 8, and 2 / 5.4.5.：
The Genus of a Group / 5.4.6.：
The genus of abelian groups / 6.1.：
Recovering a Cayley graph from any of its quotients / 6.1.1.：
A lower bound for the genus of most abelian groups / 6.1.2.：
Constructing quadrilateral imbeddings for most abelian groups / 6.1.3.：
The symmetric genus / 6.1.4.：
Rotation systems and symmetry / 6.2.1.：
Reflections / 6.2.2.：
Quotient group actions on quotient surfaces / 6.2.3.：
Alternative Cayley graphs revisited / 6.2.4.：
Group actions and imbeddings / 6.2.5.：
Are genus and symmetric genus the same? / 6.2.6.：
Euclidean space groups and the torus / 6.2.7.：
Triangle groups / 6.2.8.：
Groups of small symmetric genus / 6.2.9.：
The Riemann-Hurwitz equation revisited / 6.3.1.：
Strong symmetric genus 0 / 6.3.2.：
Symmetric genus 1 / 6.3.3.：
The geometry and algebra of groups of symmetric genus 1 / 6.3.4.：
Hurwitz's theorem / 6.3.5.：
Groups of small genus / 6.3.6.：
An example / 6.4.1.：
A face-size inequality / 6.4.2.：
Statement of main theorem / 6.4.3.：
Proof of Theorem 6.4.2: valence d = 4 / 6.4.4.：
Proof of Theorem 6.4.2: valence d = 3 / 6.4.5.：
Remarks about Theorem 6.4.2 / 6.4.6.：
References / 6.4.7.：
Bibliography
Supplementary Bibliography
Table of Notations
Subject Index
Introduction / 1.：
Representation of graphs / 1.1.：
Drawings / 1.1.1.：
12.

図書
図書
12. Graph theory : an introductory course (: us ; : gw)
Béla Bollobás
出版情報: New York ; Berlin : Springer Verlag, c1979  x, 180 p. ; 25 cm
シリーズ名: Graduate texts in mathematics ; 63
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13.

図書
図書
13. Graphs, networks, and algorithms
M.N.S. Swamy, K. Thulasiraman
出版情報: New York : Wiley, c1981  xviii, 592 p. ; 24 cm
シリーズ名: A Wiley-Interscience publication
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14.

図書
図書
14. Graph theory
W.T. Tutte ; foreword by Crispin St. J.A. Nash-Williams
出版情報: Menlo Park, Calif. : Addison-Wesley, 1984  xxi, 333 p. ; 25 cm
シリーズ名: Encyclopedia of mathematics and its applications / edited by G.-C. Rota ; v. 21 . Section, combinatorics
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15.

図書
図書
15. Applied graph theory : graphs and electrical networks. 2d rev. ed (: ne : hard - : us : pbk)
by Wai-Kai Chen
出版情報: Amsterdam : North-Holland Pub. Co. , New York : American Elsevier Pub. Co., 1976  xvi, 542 p. ; 23 cm
シリーズ名: North-Holland series in applied mathematics and mechanics ; v. 13
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16.

図書
図書
16. Examples and counterexamples in graph theory
Michael Capobianco, John C. Molluzzo ; foreword by Gary Chartrand
出版情報: New York : North-Holland New York, c1978  xii, 259 p. ; 24 cm
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17.

図書
図書
17. Extremal graph theory
Béla Bollobás
出版情報: London ; New York : Academic Press, 1978  xx, 488 p. ; 24 cm
シリーズ名: L.M.S. monographs ; 11
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目次情報: 続きを見る
Preface
Basic Definitions
Connectivity / Chapter 1：
Elementary Properties / 1.：
Menger's Theorem and its Consequences / 2.：
The Structure of 2- and 3-Connected Graphs / 3.：
Minimally k-Connected Graphs / 4.：
Graphs with Given Maximal Local Connectivity / 5.：
Exercises, Problems and Conjectures / 6.：
Matching / Chapter 2：
Fundamental Matching Theorems
The Number of 1-Factors
f-Factors
Matching in Graphs with Restrictions on the Degrees
Coverings
Cycles / Chapter 3：
Graphs with Large Minimal Degree and Large Girth
Vertex Disjoint Cycles
Edge Disjoint Cycles
The Circumference
Graphs with Cycles of Given Lengths
The Diameter / Chapter 4：
Diameter, Maximal Degree and Size
Diameter and Connectivity
Graphs with Large Subgraphs of Small Diameter
Factors of Small Diameter
Colourings / Chapter 5：
General Colouring Theorems
Critical k-Chromatic Graphs
Colouring Graphs on Surfaces
Sparse Graphs of Large Chromatic Number
Perfect Graphs
Ramsey Type Theorems
Complete Subgraphs / 7.：
The Number of Complete Subgraphs
Complete Subgraphs of r-Partite Graphs
The Structure of Graphs
The Structure of Extremal Graphs without Forbidden Subgraphs
Independent Complete Subgraphs
Topological Subgraphs / Chapter 7：
Contractions
Topological Complete Subgraphs
Semi-Topological Subgraphs
Complexity and Packing / Chapter 8：
The Complexity of Graph Properties
Monotone Properties
The Main Packing Theorem
Packing Graphs of Small Size
Applications of Packing Results to Complexity
References
Index of Symbols
Index of Definitions
Preface
Basic Definitions
Connectivity / Chapter 1：
18.

図書
図書
18. Graph theory in modern engineering : computer aided design, control, optimization, reliability analysis
Ernest J. Henley and R.A. Williams
出版情報: New York : Academic Press, 1973  xvi, 303 p. ; 23 cm
シリーズ名: Mathematics in science and engineering : a series of monographs and textbooks ; v. 98
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19.

図書
図書
19. Graph theory and computing
edited by Ronald C. Read ; contributors, Claude Berge ... [et al.]
出版情報: New York : Academic Press, 1972  xiv, 329 p. ; 23 cm
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20.

図書
図書
20. Optimization algorithms for networks and graphs
Edward Minieka
出版情報: New York : M. Dekker, c1978  viii, 356 p. ; 24 cm
シリーズ名: Industrial engineering ; v. 1
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21.

図書
図書
21. Independence theory in combinatorics : an introductory account with applications to graphs and transversals (: ; pbk.)
Victor Bryant and Hazel Perfect
出版情報: London ; New York : Chapman and Hall, 1980  xii, 144 p. ; 22 cm
シリーズ名: Chapman and Hall mathematics series
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22.

図書
図書
22. Groups and their graphs
by Israel Grossman and Wilhelm Magnus
出版情報: Washington, D.C. : Mathematical Association of America, c1964  vii, 195 p. ; 23 cm
シリーズ名: New mathematical library ; 14
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23.

図書
図書
23. Communication, transmission, and transportation networks
[by] Howard Frank [and] Ivan T. Frisch
出版情報: Reading, Mass. : Addison-Wesley Pub. Co, c1971  xiii, 479 p. ; 25 cm
シリーズ名: Addison-Wesley series in electrical engineering
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24.

図書
図書
24. Graph theory. 2nd ed (: hardcover ; : softcover)
Reinhard Diestel
出版情報: New York : Springer, c2000  xiv, 312 p. ; 24 cm
シリーズ名: Graduate texts in mathematics ; 173
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目次情報: 続きを見る
Preface
The Basics / 1：
Graphs / 1.1：
The degree of a vertex / 1.2：
Paths and cycles / 1.3：
Connectivity / 1.4：
Trees and forests / 1.5：
Bipartite graphs / 1.6：
Contraction and minors / 1 7：
Euler tours / 1.8：
Some linear algebra / 1.9：
Other notions of graphs / 1.10：
Exercises
Notes
Matching, Covering and Packing / 2：
Matching in bipartite graphs / 2.1：
Matching in general graphs(*) / 2.2：
Packing and covering / 2.3：
Tree-packing and arboricity / 2.4：
Path covers / 2.5：
2-Connected graphs and subgraphs / 3：
The structure of 3-connected graphs / 3.2：
Menger's theorem / 3.3：
Mader's theorem / 3.4：
Linking pairs of vertices / 3.5：
Planar Graphs / 4：
Topological prerequisites / 4.1：
Plane graphs / 4.2：
Drawings / 4.3：
Planar graphs: Kuratowski's theorem / 4.4：
Algebraic planarity criteria / 4.5：
Plane duality / 4.6：
Colouring / 5：
Colouring maps and planar graphs / 5.1：
Colouring vertices / 5.2：
Colouring edges / 5.3：
List colouring / 5.4：
Perfect graphs / 5.5：
Flows / 6：
Circulations(*) / 6.1：
Flows in networks / 6.2：
Group-valued flows / 6.3：
k-Flows for small k / 6.4：
Flow-colouring duality / 6.5：
Tutte's flow conjectures / 6.6：
Extremal Graph Theory / 7：
Subgraphs / 7.1：
Minors / 7.2：
Hadwiger's conjecture / 7.3：
Szemerèdi's regularity lemma / 7.4：
Applying the regularity lemma / 7.5：
Infinite Graphs / 8：
Basic notions, facts and techniques / 8.1：
Paths, trees, and ends(*) / 8.2：
Homogeneous and universal graphs / 8.3：
Connectivity and matching / 8.4：
The topological end space / 8.5：
Ramsey Theory for Graphs / 9：
Ramsey's original theorems / 9.1：
Ramsey numbers(*) / 9.2：
Induced Ramsey theorems / 9.3：
Ramsey properties and connectivity / 9.4：
Hamilton Cycles / 10：
Simple sufficient conditions / 10.1：
Hamilton cycles and degree sequences / 10.2：
Hamilton cycles in the square of a graph / 10.3：
Random Graphs / 11：
The notion of a random graph / 11.1：
The probabilistic method / 11.2：
Properties of almost all graphs / 11.3：
Threshold functions and second moments / 11.4：
Minors, Trees and WQO / 12：
Well-quasi-ordering / 12.1：
The graph minor theorem for trees / 12.2：
Tree-decompositions / 12.3：
Tree-width and forbidden minors / 12.4：
The graph minor theorem / 12.5：
A. Infinite sets
B. Surfaces Hints for all the exercises
Index
Symbol index
Sections marked by an asterisk are recommended for a first course
Of sections marked (*), the beginning is recommended for a first course
Preface
The Basics / 1：
Graphs / 1.1：
25.

図書
図書
25. Random walks on infinite graphs and groups (: hbk)
Wolfgang Woess
出版情報: Cambridge ; New York : Cambridge University Press, 2000  xi, 334 p. ; 24 cm
シリーズ名: Cambridge tracts in mathematics ; 138
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26.

図書
図書
26. A textbook of graph theory
R. Balakrishnan, K. Ranganathan
出版情報: New York : Springer, c2000  xi, 227 p. ; 25 cm
シリーズ名: Universitext
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27.

図書
図書
27. Combinatorics and graph theory
John M. Harris, Jeffry L. Hirst, Michael J. Mossinghoff
出版情報: New York : Springer, c2000  xiii, 225 p. ; 25 cm
シリーズ名: Undergraduate texts in mathematics
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目次情報: 続きを見る
Graph Theory: Introductory Concepts
Trees
Planarity
Colorings
Matchings
Ramsey Theory
References
Combinatorics: Three Basic Problems
Binomial Coefficients
The Principle of Inclusion and Exclusion
Generating Functions
Polya's Theory of Counting
More Numbers
Stable Marriage
Infinite Combinatorics and Graph Theory: Pigeons and Trees
Ramsey Revisited
ZFC
The Return of der Koenig
Ordinals, Cardinals, and Many Pigeons
Incompleteness and Coardinals
Weakly Compact Cardinals
Finite Combinatorics with Infinite Consequences
Points of Departure
Graph Theory: Introductory Concepts
Trees
Planarity
28.

図書
図書
28. A beginner's guide to graph theory (: Boston)
W.D. Wallis
出版情報: Boston : Birkhäuser, c2000  xviii, 230 p. ; 24 cm
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29.

図書
図書
29. Introductory topological analysis of electrical networks
Shu-Park Chan
出版情報: New York : Holt, Rinehart and Winston, 1969  xiv, 482 p. ; 24 cm
シリーズ名: Holt, Rinehart and Winston series in electrical engineering, electronics and systems
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30.

図書
図書
30. Modern graph theory (: hbk ; : pbk)
Béla Bollobás
出版情報: New York : Springer, c1998  xiii, 394 p. ; 25 cm
シリーズ名: Graduate texts in mathematics ; 184
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31.

図書
図書
31. Graphs, networks and algorithms
Dieter Jungnickel
出版情報: Berlin ; Tokyo : Springer, c1999  xii, 589 p. ; 24 cm
シリーズ名: Algorithms and computation in mathematics ; v. 5
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32.

図書
図書
32. Graphes et hypergraphes
Claude Berge
出版情報: Paris : Dunod, c1970  xviii, 502 p ; 25 cm
シリーズ名: Monographies universitaires de mathématiques ; 37
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33.

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図書
33. Graphical models for machine learning and digital communication
Brendan J. Frey
出版情報: Cambridge, Mass : The MIT Press, c1998  xiii, 195 p. ; 24 cm
シリーズ名: Adaptive computation and machine learning
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目次情報: 続きを見る
Preface
Introduction / 1：
A probabilistic perspective / 1.1：
Pattern classification / 1.1.1：
Unsupervised learning / 1.1.2：
Data compression / 1.1.3：
Channel coding / 1.1.4：
Probabilistic inference / 1.1.5：
Graphical models: Factor graphs, Markov random fields and Bayesian belief networks / 1.2：
Factor graphs / 1.2.1：
Markov random fields / 1.2.2：
Bayesian networks / 1.2.3：
Ancestral simulation in Bayesian networks / 1.2.4：
Dependency separation in Bayesian networks / 1.2.5：
Example 1: Recursive convolutional codes and turbocodes / 1.2.6：
Parameterized Bayesian networks / 1.2.7：
Example 2: The bars problem / 1.2.8：
Organization of this book / 1.3：
Probabilistic Inference in Graphical Models / 2：
Exact inference using probability propagation (the sum-product algorithm) / 2.1：
The generalized forward-backward algorithm / 2.1.1：
The burglar alarm problem / 2.1.2：
Probability propagation (the sum-product algorithm) / 2.1.3：
Grouping and duplicating variables in Bayesian networks / 2.1.4：
Exact inference in multiply-connected networks is NP-hard / 2.1.5：
Monte Carlo inference: Gibbs sampling and slice sampling / 2.2：
Inference by ancestral simulation in Bayesian networks / 2.2.1：
Gibbs sampling / 2.2.2：
Gibbs sampling for the burglar alarm problem / 2.2.3：
Slice sampling for continuous variables / 2.2.4：
Variational inference / 2.3：
Choosing the distance measure / 2.3.1：
Choosing the form of the variational distribution / 2.3.2：
Variational inference for the burglar alarm problem / 2.3.3：
Bounds and extended representations / 2.3.4：
Helmholtz machines / 2.4：
Factorial recognition networks / 2.4.1：
Nonfactorial recognition networks / 2.4.2：
The stochastic Helmholtz machine / 2.4.3：
A recognition network that solves the burglar alarm problem / 2.4.4：
Pattern Classification / 3：
Bayesian networks for pattern classification / 3.1：
Autoregressive networks / 3.2：
The logistic autoregressive network / 3.2.1：
MAP estimation for autoregressive networks / 3.2.2：
Scaled priors in logistic autoregressive networks / 3.2.3：
Ensembles of autoregressive networks / 3.2.4：
Estimating latent variable models using the EM algorithm / 3.3：
The expectation maximization (EM) algorithm / 3.3.1：
The generalized expectation maximization algorithm / 3.3.2：
Multiple-cause networks / 3.4：
Estimation by iterative probability propagation / 3.4.1：
Estimation by Gibbs sampling / 3.4.2：
Generalized EM using variational inference / 3.4.3：
Hierarchical networks / 3.4.4：
Ensembles of networks / 3.4.6：
Classification of handwritten digits / 3.5：
Logistic autoregressive classifiers: LARC-1,ELARC-1 / 3.5.1：
The Gibbs machine: GM-1 / 3.5.2：
The mean field Bayesian network: MFBN-1 / 3.5.3：
Stochastic Helmholtz machines: SHM-1, SHM-2, ESHM-1 / 3.5.4：
The classification and regression tree: CART-1 / 3.5.5：
The naive Bayes classifier: NBAYESC-1 / 3.5.6：
The k-nearest neighbor classifier: KNN-CLASS-1 / 3.5.7：
Results / 3.5.8：
Unsupervised Learning / 4：
Extracting structure from images using the wake-sleep algorithm / 4.1：
Wake-sleep parameter estimation / 4.1.1：
Automatic clean-up of noisy images / 4.1.2：
Wake-sleep estimation without positive parameter constraints / 4.1.3：
How hard is the bars problem? / 4.1.4：
Simultaneous extraction of continuous and categorical structure / 4.2：
Continuous sigmoidal Bayesian networks / 4.2.1：
Inference using slice sampling / 4.2.2：
Parameter estimation using slice sampling / 4.2.3：
Nonlinear Gaussian Bayesian networks (NLGBNs) / 4.3：
The model / 4.3.1：
Variational inference and learning / 4.3.2：
Results on the continuous stereo disparity problem / 4.3.3：
Pattern classification using the variational bound / 4.3.4：
Data Compression / 5：
Fast compression with Bayesian networks / 5.1：
Communicating extra information through the codeword choice / 5.2：
Example: A simple mixture model / 5.2.1：
The optimal bits-back coding rate / 5.2.2：
Suboptimal bits-back coding / 5.2.3：
Relationship to maximum likelihood estimation / 5.3：
The "bits-back" coding algorithm / 5.4：
The bits-back coding algorithm with feedback / 5.4.1：
Queue drought in feedback encoders / 5.4.2：
Experimental results / 5.5：
Bits-back coding with a multiple-cause model / 5.5.1：
Compressing handwritten digits / 5.5.2：
Integrating over model parameters using bits-back coding / 5.6：
Channel Coding / 6：
Review: Simplifying the playing field / 6.1：
Additive white Gaussian noise (AWGN) / 6.1.1：
Capacity of an AWGN channel / 6.1.2：
Signal constellations / 6.1.3：
Linear binary codes can get us to capacity / 6.1.4：
Bit error rate (BER) and signal-to-noise ratio (Eb/N0) / 6.1.5：
Capacity of an AWGN channel with binary signalling / 6.1.6：
Achievable BER for an AWGN channel with binary signalling / 6.1.7：
Graphical models for error correction: Turbocodes, low-density parity-check codes and more / 6.2：
Hamming codes / 6.2.1：
Convolutional codes / 6.2.2：
Decoding convolutional codes by probability propagation / 6.2.3：
Turbocodes: parallel concatenated convolutional codes / 6.2.4：
Serially-concatenated convolutional codes, low-density parity-check codes, and product codes / 6.2.5：
"A code by any other network would not decode as sweetly" / 6.3：
Trellis-constrained codes (TCCs) / 6.4：
Homogeneous trellis-constrained codes / 6.4.1：
Ring-connected trellis-constrained codes / 6.4.2：
Decoding complexity of iterative decoders / 6.5：
Parallel iterative decoding / 6.6：
Concurrent turbodecoding / 6.6.1：
Speeding up iterative decoding by detecting variables early / 6.6.2：
Early detection / 6.7.1：
Early detection for turbocodes: Trellis splicing / 6.7.2：
Future Research Directions / 6.7.3：
Modularity and abstraction / 7.1：
Faster inference and learning / 7.2：
Scaling up to the brain / 7.3：
Improving model structures / 7.4：
Iterative decoding / 7.5：
Iterative decoding in the real world / 7.6：
Unification / 7.7：
References
Index
Preface
Introduction / 1：
A probabilistic perspective / 1.1：
34.

図書
図書
34. Graph drawing : algorithms for the visualization of graphs
Giuseppe Di Battista ... [et al.]
出版情報: Upper Saddle River, N.J. : Prentice Hall, c1999  xi, 397 p. ; 25 cm
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目次情報: 続きを見る
Graphs and Their Drawings / 1：
Paradigms for Graph Drawing / 2：
Divide and Conquer / 3：
Planar Orientations / 4：
Flow and Orthogonal Drawings / 5：
Flow and Upward Planarity / 6：
Incremental Construction / 7：
Nonplanar Orientations / 8：
Layered Drawings of Digraphs / 9：
Force Directed Methods / 10：
Proving Lower Bounds / 11：
A Bounds / Appendix：
Bibliography
Index
Graphs and Their Drawings / 1：
Paradigms for Graph Drawing / 2：
Divide and Conquer / 3：
35.

図書
図書
35. Geometry of cuts and metrics
Michel Marie Deza, Monique Laurent
出版情報: Berlin : Springer-Verlag, c1997  xii, 587 p. ; 24 cm
シリーズ名: Algorithms and combinatorics ; 15
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36.

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図書
36. Combinatorics with emphasis on the theory of graphs (: us ; : gw)
Jack E. Graver, Mark E. Watkins
出版情報: New York ; Berlin : Springer, c1977  xx, 351 p. ; 25 cm
シリーズ名: Graduate texts in mathematics ; 54
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37.

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図書
37. Graph theory (: hardcover ; : softcover)
Reinhard Diestel
出版情報: New York : Springer, 1997  xiv, 286 p. ; 25 cm
シリーズ名: Graduate texts in mathematics ; 173
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目次情報: 続きを見る
Preface
The Basics / 1：
Graphs / 1.1：
The degree of a vertex / 1.2：
Paths and cycles / 1.3：
Connectivity / 1.4：
Trees and forests / 1.5：
Bipartite graphs / 1.6：
Contraction and minors / 1 7：
Euler tours / 1.8：
Some linear algebra / 1.9：
Other notions of graphs / 1.10：
Exercises
Notes
Matching, Covering and Packing / 2：
Matching in bipartite graphs / 2.1：
Matching in general graphs(*) / 2.2：
Packing and covering / 2.3：
Tree-packing and arboricity / 2.4：
Path covers / 2.5：
2-Connected graphs and subgraphs / 3：
The structure of 3-connected graphs / 3.2：
Menger's theorem / 3.3：
Mader's theorem / 3.4：
Linking pairs of vertices / 3.5：
Planar Graphs / 4：
Topological prerequisites / 4.1：
Plane graphs / 4.2：
Drawings / 4.3：
Planar graphs: Kuratowski's theorem / 4.4：
Algebraic planarity criteria / 4.5：
Plane duality / 4.6：
Colouring / 5：
Colouring maps and planar graphs / 5.1：
Colouring vertices / 5.2：
Colouring edges / 5.3：
List colouring / 5.4：
Perfect graphs / 5.5：
Flows / 6：
Circulations(*) / 6.1：
Flows in networks / 6.2：
Group-valued flows / 6.3：
k-Flows for small k / 6.4：
Flow-colouring duality / 6.5：
Tutte's flow conjectures / 6.6：
Extremal Graph Theory / 7：
Subgraphs / 7.1：
Minors / 7.2：
Hadwiger's conjecture / 7.3：
Szemerèdi's regularity lemma / 7.4：
Applying the regularity lemma / 7.5：
Infinite Graphs / 8：
Basic notions, facts and techniques / 8.1：
Paths, trees, and ends(*) / 8.2：
Homogeneous and universal graphs / 8.3：
Connectivity and matching / 8.4：
The topological end space / 8.5：
Ramsey Theory for Graphs / 9：
Ramsey's original theorems / 9.1：
Ramsey numbers(*) / 9.2：
Induced Ramsey theorems / 9.3：
Ramsey properties and connectivity / 9.4：
Hamilton Cycles / 10：
Simple sufficient conditions / 10.1：
Hamilton cycles and degree sequences / 10.2：
Hamilton cycles in the square of a graph / 10.3：
Random Graphs / 11：
The notion of a random graph / 11.1：
The probabilistic method / 11.2：
Properties of almost all graphs / 11.3：
Threshold functions and second moments / 11.4：
Minors, Trees and WQO / 12：
Well-quasi-ordering / 12.1：
The graph minor theorem for trees / 12.2：
Tree-decompositions / 12.3：
Tree-width and forbidden minors / 12.4：
The graph minor theorem / 12.5：
A. Infinite sets
B. Surfaces Hints for all the exercises
Index
Symbol index
Sections marked by an asterisk are recommended for a first course
Of sections marked (*), the beginning is recommended for a first course
Preface
The Basics / 1：
Graphs / 1.1：
38.

図書
図書
38. Truth functions and the problem of their realization by two-terminal graphs
by A. Ádám ; [Rev. by M. Makkai and F. Móricz]
出版情報: Budapest : Akadémiai Kiadó, 1968  206 p. ; 25 cm
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39. Algèbre moderne et théorie des graphes orientées vers les sciences économiques et sociales (v. 1 ; v. 2)
par Bernard Roy ; contribution de Michel Horps
出版情報: Paris : Dunod, 1969-70  2 v ; 24 cm
シリーズ名: Finance et économie appliquée ; 31-32
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目次情報:
t. 1. Notions et résultats fondamentaux
t. 2. Applications et problèmes spécifiques
t. 1. Notions et résultats fondamentaux
t. 2. Applications et problèmes spécifiques
40.

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図書
40. Bounded incremental computation
G. Ramalingam
出版情報: Berlin : Springer, c1996  xi, 190 p. ; 24 cm
シリーズ名: Lecture notes in computer science ; 1089
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41.

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図書
41. Embeddability in graphs (: cc ; : ne)
Liu Yanpei
出版情報: Beijing : Science Press , Dordrecht : Kluwer Academic Publishers, c1995  xvi, 398 p. ; 25 cm
シリーズ名: Mathematics and its applications ; v. 338 . China series
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42.

図書
図書
42. Eigenspaces of graphs
D. Cvetković, P. Rowlinson, S. Simić
出版情報: Cambridge : Cambridge University Press, 1997  xiii, 258 p. ; 24 cm
シリーズ名: Encyclopedia of mathematics and its applications / edited by G.-C. Rota ; v. 66
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A background in graph spectra / 1：
Eigenvectors of graphs / 2：
Eigenvectors of techniques / 3：
Graph angles / 4：
Angle techniques / 5：
Graph perturbations / 6：
Star partitions / 7：
Canonical star bases / 8：
Miscellaneous results / 9：
A background in graph spectra / 1：
Eigenvectors of graphs / 2：
Eigenvectors of techniques / 3：
43.

図書
図書
43. Discrete structures of computer science
Leon S. Levy
出版情報: New York : Wiley, c1980  310 p. ; 24 cm
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44.

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図書
44. Applications of graph theory algorithms
Vinod Chachra, Prabhakar M. Ghare, James M. Moore
出版情報: New York : North-Holland-New York, c1979  ix, 421 p. ; 24 cm
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45.

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図書
45. Graphs and genes (: gw ; : us)
B. G. Mirkin, S. N. Rodin ; translated from the Russian by H. Lynn Beus
出版情報: Berlin : Springer-Verlag, 1984  xiv, 197 p. ; 25 cm
シリーズ名: Biomathematics ; v. 11
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46.

図書
図書
46. Problems in combinatorics and graph theory
Ioan Tomescu ; translated from Romanian by Robert A. Melter
出版情報: New York : Wiley, c1985  xvii, 335 p. ; 25 cm
シリーズ名: Wiley-Interscience series in discrete mathematics
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47.

図書
図書
47. Graph theory with applications
J.A. Bondy and U.S.R. Murty
出版情報: New York : North Holland, 1976  x, 264 p. ; 24 cm
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48.

図書
図書
48. Chemical graph theory (v. 1 ; v. 2)
Nenad Trinajstić
出版情報: Boca Raton, Fla. : CRC Press, c1983  2 v. ; 27 cm
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49.

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図書
49. Completeness, confluence, and related properties of clause graph resolution (: Kaufmann ; : Pitman)
Norbert Eisinger
出版情報: London : Pitman , San Mateo, Calif. : Morgan Kaufmann, 1991  181 p. ; 25 cm
シリーズ名: Research notes in artificial intelligence
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50.

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図書
50. Chemical graph theory. 2nd ed
Nenad Trinajstić
出版情報: Boca Raton ; Tokyo : CRC Press, c1992  322 p. ; 25 cm
シリーズ名: Mathematical chemistry series
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