THEORY AND APPLICATION OF GRAPHS

This book considers a graph as a mathematical structure on a set of elements with a binary relation, and provides the most classical and important theory and application of graphs. It covers basic concepts, trees and graphic spaces, plane graphs and planar graphs, flows and connectivity, matchings and independent sets, coloring theory, graphs and groups. These topics, both theoretical and applied, are treated with some depth and with some suggestions for further reading. The treatment of material particularly lays stress on digraphs, the mutual connections among these topics and the equivalence of some well-known theorems. All theorems are stated clearly, together with full and concise proofs. A number of examples, more than 350 figures and more than 500 exercises are given to help the reader understand and examine the materials covered in the book.