Algebraic graph theory : morphisms, monoids, and matrices / by Ulrich Knauer.

Format:

Book

Author/Creator:

Knauer, Ulrich, 1942-

Series:

De Gruyter studies in mathematics ; 41.

De Gruyter studies in mathematics ; 41

Language:

English

Subjects (All):

Graph theory.

Algebraic topology.

Physical Description:

1 online resource (324 p.)

Edition:

1st ed.

Place of Publication:

Berlin ; Boston : De Gruyter, c2011.

Language Note:

English

Summary:

Graph models are extremely useful for almost all applications and applicators as they play an important role as structuring tools. They allow to model net structures - like roads, computers, telephones - instances of abstract data structures - like lists, stacks, trees - and functional or object oriented programming. In turn, graphs are models for mathematical objects, like categories and functors. This highly self-contained book about algebraic graph theory is written with a view to keep the lively and unconventional atmosphere of a spoken text to communicate the enthusiasm the author feels about this subject. The focus is on homomorphisms and endomorphisms, matrices and eigenvalues. It ends with a challenging chapter on the topological question of embeddability of Cayley graphs on surfaces.

Contents:

Frontmatter

Preface

Contents

Chapter 1. Directed and undirected graphs

Chapter 2. Graphs and matrices

Chapter 3. Categories and functors

Chapter 4. Binary graph operations

Chapter 5. Line graph and other unary graph operations

Chapter 6. Graphs and vector spaces

Chapter 7. Graphs, groups and monoids

Chapter 8. The characteristic polynomial of graphs

Chapter 9. Graphs and monoids

Chapter 10. Compositions, unretractivities and monoids

Chapter 11. Cayley graphs of semigroups

Chapter 12. Vertex transitive Cayley graphs

Chapter 13. Embeddings of Cayley graphs - genus of semigroups

Bibliography

Index

Index of symbols

Notes:

Description based upon print version of record.

Includes bibliographical references and index.

ISBN:

9786613400444

9781283400442

1283400448

9783110255096

311025509X

OCLC:

757261228