The theory of 2-structures : a framework for decomposition and transformation of graphs

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The theory of 2-structures : a framework for decomposition and transformation of graphs / A. Ehrenfeucht, T. Harju, G. Rozenberg

資料種別:

図書

出版情報:

Singapore : World Scientific, c1999

形態:

xvi, 290 p. ; 23 cm

著者名:

ISBN:

9789810240424 [9810240422]

書誌ID:

BA4349070X

子書誌情報

フルテキスト

所蔵情報

他の版・巻

書誌詳細

注記:

Includes bibliographical references (p. 269-277) and index

言語:

英語

目次情報:

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：

Sets and functions / 1.1.1：

Closure operators / 1.1.2：

Relations / 1.1.3：

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