Introduction

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.

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