Algebraic Graph Theory: Morphisms, Monoids and Matrices

Ulrich Knauer; Kolja Knauer

Published by De Gruyter 2019

Algebraic Graph Theory

Morphisms, Monoids and Matrices

Ulrich Knauer and Kolja Knauer

Volume 41 in the series De Gruyter Studies in Mathematics

https://doi.org/10.1515/9783110617368

Overview
Contents

About this book

Graph models are extremely useful for a large number of applications as they play an important role as structuring tools. They allow to model net structures – like roads, computers, telephones, social networks – instances of abstract data structures – like lists, stacks, trees – and functional or object oriented programming. The focus of this highly self-contained book is on homomorphisms and endomorphisms, matrices and eigenvalues.

Discusses connections between graphs and semigroups/monoids.
Studies several types of graph morphisms which are of interest for many applications.
New material includes characteristics and current results on Cayley graphs, and new figures.

Author / Editor information

Ulrich Knauer, Carl von Ossietzky Universität Oldenburg, Germany; Kolja Knauer, Université Aix-Marseille, France.

Topics

Frontmatter Publicly Available Download PDF	I
Preface Publicly Available Download PDF	V
Preface For The Second Edition Publicly Available Download PDF	XI
Contents Publicly Available Download PDF	XIII
1. Directed And Undirected Graphs Requires Authentication Unlicensed Licensed Download PDF	1
2. Graphs And Matrices Requires Authentication Unlicensed Licensed Download PDF	29
3. Categories And Functors Requires Authentication Unlicensed Licensed Download PDF	49
4. Binary Graph Operations Requires Authentication Unlicensed Licensed Download PDF	65
5. Line Graph And Other Unary Graph Operations Requires Authentication Unlicensed Licensed Download PDF	91
6. Graphs And Vector Spaces Requires Authentication Unlicensed Licensed Download PDF	105
7. Graphs, Groups, And Monoids Requires Authentication Unlicensed Licensed Download PDF	137
8. The Characteristic Polynomial Of Graphs Requires Authentication Unlicensed Licensed Download PDF	163
9. Graphs And Semigroups Requires Authentication Unlicensed Licensed Download PDF	183
10. Compositions, Unretractivities, And Monoids Requires Authentication Unlicensed Licensed Download PDF	209
11. Cayley Graphs Of Semigroups Requires Authentication Unlicensed Licensed Download PDF	225
12. Vertex Transitive Cayley Graphs Requires Authentication Unlicensed Licensed Download PDF	247
13. Embeddings Of Cayley Graphs—Genus Of Semigroups Requires Authentication Unlicensed Licensed Download PDF	261
List Of Cited Papers, Theses Etc Requires Authentication Unlicensed Licensed Download PDF	303
List Of Books Requires Authentication Unlicensed Licensed Download PDF	307
Index Requires Authentication Unlicensed Licensed Download PDF	319
Index Of Symbols Requires Authentication Unlicensed Licensed Download PDF	327

(Deutsch)

Language: English
Publisher: De Gruyter
Edition: 2nd rev. and ext. ed.
Audience: Graduate students and researchers in mathematics and computer science.
Pages
- Front matter: 18
- Main content: 331
Illustrations
- Illustrations: 145
- Tables: 20
Keywords: Algebraic; Graph Theory; Matrices; Monoids; Morphisms

eBook

Published: October 8, 2019
ISBN: 9783110617368

Hardcover

Published: October 8, 2019
ISBN: 9783110616125