#### A First Course in Graph Theory

by Gary Chartrand, Ping Zhang

Optional sections designated as "excursion" and "exploration" present interesting sidelights of graph theory and touch upon topics that allow students the opportunity to experiment and use their imaginations. Three appendixes review important facts about sets and logic, equivalence relations and functions, and the methods of proof. The text concludes with solutions or hints for odd-numbered exercises, in addition to references, indexes, and a list of symbols.

#### Introductory Graph Theory

by Gary Chartrand

Graph theory is used today in the physical sciences, social sciences, computer science, and other areas. *Introductory Graph Theory* presents a nontechnical introduction to this exciting field in a clear, lively, and informative style.

Author Gary Chartrand covers the important elementary topics of graph theory and its applications. In addition, he presents a large variety of proofs designed to strengthen mathematical techniques and offers challenging opportunities to have fun with mathematics.

Ten major topics ? profusely illustrated ? include: Mathematical Models, Elementary Concepts of Graph Theory, Transportation Problems, Connection Problems, Party Problems, Digraphs and Mathematical Models, Games and Puzzles, Graphs and Social Psychology, Planar Graphs and Coloring Problems, and Graphs and Other Mathematics.

A useful Appendix covers Sets, Relations, Functions, and Proofs, and a section devoted to exercises ? with answers, hints, and solutions ? is especially valuable to anyone encountering graph theory for the first time.

Undergraduate mathematics students at every level, puzzlists, and mathematical hobbyists will find well-organized coverage of the fundamentals of graph theory in this highly readable and thoroughly enjoyable book.

#### Introduction to Graph Theory

by Gary Chartrand, Ping Zhang

#### Chromatic Graph Theory

by Gary Chartrand, Ping Zhang

Beginning with the origin of the four color problem in 1852, the field of graph colorings has developed into one of the most popular areas of graph theory. Introducing graph theory with a coloring theme, Chromatic Graph Theory explores connections between major topics in graph theory and graph colorings as well as emerging topics.

This self-contained book first presents various fundamentals of graph theory that lie outside of graph colorings, including basic terminology and results, trees and connectivity, Eulerian and Hamiltonian graphs, matchings and factorizations, and graph embeddings. The remainder of the text deals exclusively with graph colorings. It covers vertex colorings and bounds for the chromatic number, vertex colorings of graphs embedded on surfaces, and a variety of restricted vertex colorings. The authors also describe edge colorings, monochromatic and rainbow edge colorings, complete vertex colorings, several distinguishing vertex and edge colorings, and many distance-related vertex colorings.

With historical, applied, and algorithmic discussions, this text offers a solid introduction to one of the most popular areas of graph theory.