Algebraic Graph Theory : : Morphisms, Monoids and Matrices / / Ulrich Knauer.

• Superior document: Title is part of eBook package: De Gruyter DG Studies in Mathematics eBook-Package
• VerfasserIn: Knauer, Ulrich,
• Place / Publishing House: Berlin ;, Boston : : De Gruyter, , [2011]; ©2011
• Year of Publication: 2011
• Language: English
• Series: De Gruyter Studies in Mathematics , 41
• Physical Description: 1 online resource (308 p.)

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.

Table of 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