Textbook in PDF format

This book studies algebraic representations of graphs in order to investigate combinatorial structures via local symmetries. Topological, combinatorial and algebraic classifications are distinguished by invariants of polynomial type and algorithms are designed to determine all such classifications with complexity analysis. Being a summary of the author´s original work on graph embeddings, this book is an essential reference for researchers in graph theory.
Preface (DG Edition)
Preface (USTC Edition)
Contents
Abstract Graphs
Abstract Maps
Duality
Orientability
Orientable Maps
Nonorientable Maps
Isomorphisms of Maps
Asymmetrization
Asymmetrized Petal Bundles
Asymmetrized Maps
Maps within Symmetry
Genus Polynomials
Census with Partitions
Equations with Partitions
Upper Maps of a Graph
Genera of a Graph
Isogemial Graphs
Surface Embeddability
Appendix 1: Concepts of Polyhedra, Surfaces, Embeddings and Maps
Appendix 2: Table of Genus Polynomials for Embeddings and Maps of Small Size
Appendix 3: Atlas of Rooted and Unrooted Maps for Small Graphs
Bibliography
Author Index
Subject Index