(Ebook) Algebraic Graph Theory: Morphisms, Monoids and Matrices by Ulrich Knauer ISBN 9783110254082, 3110254085, 9783110254081

(Ebook) Algebraic Graph Theory: Morphisms, Monoids and Matrices by Ulrich Knauer ISBN 9783110254082, 3110254085, 9783110254081

Mathematics Subject Classification 2010: • 05C05 Trees • 05C10 Planar graphs; geometric and topological aspects of graph theory • 05C12 Distance in graphs • 05C20 Directed graphs (digraphs), tournaments • 05C25 Graphs and abstract algebra (groups, rings, fields, etc.) • 05C38 Paths and cycles • 05C50 Graphs and linear algebra (matrices, eigenvalues, etc.) • 05C62 Graph representations (geometric and intersection representations, etc.) • 05C75 Structural characterization of families of graphs • 05C90 Applications of graph theory • 20M17 Regular semigroups • 20M19 Orthodox semigroups • 20M20 Semigroups of transformations, relations, partitions, etc. • 20M30 Representation of semigroups; actions of semigroups on sets • 18B10 Categories of spans/cospans, relations, or partial maps • 18B40 Groupoids, semigroupoids, semigroups, groups (viewed as categories)

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.