Algebraic Graph Theory: Morphisms, Monoids and Matrices

Ulrich Knauer

Published by De Gruyter 2011

Algebraic Graph Theory

Morphisms, Monoids and Matrices

Ulrich Knauer

Volume 41 in the series De Gruyter Studies in Mathematics

https://doi.org/10.1515/9783110255096

Overview
Contents

About this book

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.

Author / Editor information

Ulrich Knauer, Carl von Ossietzky Universität Oldenburg, Germany.

Supplementary Materials

Errata

Topics

Frontmatter Requires Authentication Unlicensed Licensed Download PDF	I
Preface Requires Authentication Unlicensed Licensed Download PDF	V
Contents Requires Authentication Unlicensed Licensed Download PDF	XI
Chapter 1. Directed and undirected graphs Requires Authentication Unlicensed Licensed Download PDF	1
Chapter 2. Graphs and matrices Requires Authentication Unlicensed Licensed Download PDF	26
Chapter 3. Categories and functors Requires Authentication Unlicensed Licensed Download PDF	48
Chapter 4. Binary graph operations Requires Authentication Unlicensed Licensed Download PDF	64
Chapter 5. Line graph and other unary graph operations Requires Authentication Unlicensed Licensed Download PDF	91
Chapter 6. Graphs and vector spaces Requires Authentication Unlicensed Licensed Download PDF	104
Chapter 7. Graphs, groups and monoids Requires Authentication Unlicensed Licensed Download PDF	136
Chapter 8. The characteristic polynomial of graphs Requires Authentication Unlicensed Licensed Download PDF	161
Chapter 9. Graphs and monoids Requires Authentication Unlicensed Licensed Download PDF	181
Chapter 10. Compositions, unretractivities and monoids Requires Authentication Unlicensed Licensed Download PDF	208
Chapter 11. Cayley graphs of semigroups Requires Authentication Unlicensed Licensed Download PDF	225
Chapter 12. Vertex transitive Cayley graphs Requires Authentication Unlicensed Licensed Download PDF	245
Chapter 13. Embeddings of Cayley graphs – genus of semigroups Requires Authentication Unlicensed Licensed Download PDF	261
Bibliography Requires Authentication Unlicensed Licensed Download PDF	285
Index Requires Authentication Unlicensed Licensed Download PDF	301
Index of symbols Requires Authentication Unlicensed Licensed Download PDF	307

(Deutsch)

Language: English
Publisher: De Gruyter
Audience: Graduate and Advances Undergraduate Students of Mathematics and Computer Sciences, Researchers; Academic Libraries
Pages
- Front matter: 16
- Main content: 308
Illustrations
- Tables: 6
Keywords: Graph Theory; Algebra; Matrices; Monoids; Morphisms

eBook

Published: September 29, 2011
ISBN: 9783110255096