Preface |
Preliminaries / Chapter 1: |
Notations / 1.1: |
Sets and functions / 1.1.1: |
Closure operators / 1.1.2: |
Relations / 1.1.3: |
Equivalence relations / 1.1.4: |
Partial orders / 1.2: |
Downsets / 1.2.1: |
Order embeddings / 1.2.2: |
Linear orders / 1.2.3: |
Semigroups and groups / 1.3: |
Notations for semigroups and monoids / 1.3.1: |
Free monoids (with involution) / 1.3.2: |
Preliminaries on groups / 1.3.3: |
Group actions / 1.3.4: |
Free groups, commutators and verbal identities / 1.3.5: |
Graph Theoretical Preliminaries / Chapter 2: |
Directed and Undirected Graphs / 2.1: |
Basic notions / 2.1.1: |
Connectivity of graphs / 2.1.2: |
Some special graphs / 2.1.3: |
Comparability graphs / 2.2: |
Transitively oriented graphs / 2.2.1: |
Permutation graphs and cographs / 2.2.2: |
Construction trees of cographs / 2.2.3: |
2-Structures and Their Clans / Chapter 3: |
Introduction and representations / 3.1: |
Definition of a 2-structure / 3.1.1: |
Isomorphic 2-structures / 3.1.2: |
Reversibility / 3.1.3: |
Substructures and clans / 3.2: |
Substructures, clans and factors / 3.2.1: |
Refinements and similarity / 3.2.2: |
Reversible version / 3.2.3: |
Graphs and packed components / 3.2.4: |
Some special 2-structures / 3.2.5: |
Closure properties of clans / 3.3: |
Basic closures / 3.3.1: |
Sibas: set theoretic closure properties / 3.3.2: |
Clans of factors / 3.3.3: |
Prime clans / 3.4: |
Prime members in sibas / 3.4.1: |
Minimal overlapping clans / 3.4.2: |
Quotients and Homomorphisms / Chapter 4: |
Quotients / 4.1: |
Factorizations and quotients / 4.1.1: |
Homomorphisms / 4.1.2: |
Natural epimorphisms and decompositions / 4.1.3: |
Clans and epimorphisms / 4.2: |
Homomorphism theorem / 4.2.1: |
Prime clans in quotients / 4.2.2: |
Primitive quotients / 4.2.3: |
Other operations / 4.3: |
Premorphisms / 4.3.1: |
Extensions / 4.3.2: |
Clan Decomposition / Chapter 5: |
The clan decomposition theorem / 5.1: |
Maximal prime clans / 5.1.1: |
Special sibas and 2-structures / 5.1.2: |
The relationship of sibas to 2-structures / 5.1.3: |
The shape of a 2-structure / 5.2: |
The shape and its representation as a tree / 5.2.1: |
Same shapes / 5.2.2: |
A construction of prime clans / 5.3: |
A construction of clans / 5.3.1: |
Primitive 2-Structures / 5.3.2: |
Small primitive substructures / 6.1: |
Uniformly imprimitive 2-structures / 6.1.1: |
Primitive substructures of 3 or 4 nodes / 6.1.2: |
Hereditary properties / 6.2: |
Local and global nodes / 6.2.1: |
Critically primitive 2-structures / 6.2.2: |
The parity theorem / 6.3.1: |
The list of critically primitive 2-structures / 6.3.2: |
Angular 2-Structures / Chapter 7: |
Angularity / 7.1: |
All-connectivity / 7.1.1: |
All-connected skew angular 2-structures / 7.1.2: |
T-structures / 7.2: |
T-structures and partial orders / 7.2.1: |
T[subscript 2]-structures / 7.2.2: |
Linear orders and Schroder numbers / 7.3: |
Bi-orders and linear orders / 7.3.1: |
Uniformly imprimitive linear orders / 7.3.2: |
Parenthesis words and Schroder numbers / 7.3.3: |
Labelled 2-Structures / Chapter 8: |
Introduction to l2-structures / 8.1: |
Definitions / 8.1.1: |
Substructures, clans and quotients / 8.1.2: |
Clan decomposition of l2-structures / 8.2: |
Uniqueness of decompositions / 8.2.1: |
The shape of an l2-structure / 8.2.2: |
Graphs and their representations / 8.2.3: |
Graphs as l2-structures / 8.3.1: |
On comparability graphs / 8.3.2: |
Unstable Labelled 2-Structures / Chapter 9: |
Triangle free and unstable l2-structures / 9.1: |
Removable edges / 9.1.1: |
Internal and external nodes / 9.1.2: |
Triangle-free l2-structures / 9.1.3: |
Heredity in unstable l2-structures / 9.2: |
The partition of nodes / 9.2.1: |
Alternating structures / 9.2.2: |
Degrees of nodes / 9.2.3: |
A composition of unstable l2-structures / 9.3: |
A constructive reduction of primitive l2-structures / 9.3.1: |
Pendant components / 9.3.2: |
Automorphisms of Labelled 2-Structures / Chapter 10: |
Label preserving automorphisms / 10.1: |
The l-automorphism groups / 10.1.1: |
Transitivity / 10.1.2: |
Automorphic actions on factors / 10.1.3: |
Universality of l-automorphism groups / 10.1.4: |
Nonpreserving automorphisms / 10.2: |
Connections to l-automorphisms / 10.2.1: |
Transitivity and associated permutations / 10.2.2: |
Representing labels by automorphisms / 10.2.3: |
Switching of Graphs / Chapter 11: |
Introduction to switching / 11.1: |
The group of graphs / 11.1.1: |
Switching classes / 11.1.3: |
Structural properties of switching classes / 11.2: |
A local characterization / 11.2.1: |
Automorphisms / 11.2.2: |
Special problems on undirected graphs / 11.3: |
Two-graphs / 11.3.1: |
Eulerian graphs / 11.3.2: |
Pancyclic graphs / 11.3.3: |
Trees / 11.3.4: |
Labelled Structures over Groups / Chapter 12: |
Introduction / 12.1: |
Groups and involutions / 12.1.1: |
Selectors and switching classes / 12.1.2: |
An interpretation in networks / 12.2: |
Concurrent behaviour in networks / 12.2.1: |
Reducing the actions to groups / 12.2.2: |
Introducing reversibility / 12.2.3: |
Examples for some special groups / 12.3: |
The cyclic groups Z[subscript 3] and Z[subscript 4] / 12.3.1: |
The symmetric group S[subscript 3] / 12.3.2: |
Clans of Switching Classes / Chapter 13: |
Associated groups / 13.1: |
The group of selectors / 13.1.1: |
The group of abelian switching classes / 13.1.2: |
Clans and horizons / 13.2: |
Spanning trees / 13.2.1: |
Horizons and constant selectors / 13.2.2: |
Clans / 13.2.3: |
Cardinalities of switching classes / 13.3: |
Some special cases / 13.3.1: |
Centralizers / 13.3.2: |
Some improvements / 13.3.3: |
Quotients and Plane Trees / Chapter 14: |
Quotients of switching classes / 14.1: |
Planes and plane trees / 14.1.1: |
Planes / 14.2.1: |
Plane trees / 14.2.2: |
Bijective correspondence of plane trees / 14.2.3: |
Forms / 14.2.4: |
Invariants / Chapter 15: |
Free invariants / 15.1: |
General invariants / 15.1.1: |
Edge monoids / 15.1.2: |
Variable functions and free invariants / 15.1.3: |
Group properties of free invariants / 15.2: |
Abelian property / 15.2.1: |
Graphs of words / 15.2.2: |
Verbal identities / 15.2.3: |
Invariants on abelian groups / 15.3: |
Independency of free invariants / 15.3.1: |
Complete sets of invariants / 15.3.2: |
Invariants on nonabelian groups / 15.4: |
General observations / 15.4.1: |
Central characters / 15.4.2: |
A characterization theorem / 15.4.3: |
Bibliography |
Index |
Preface |
Preliminaries / Chapter 1: |
Notations / 1.1: |