Chartrand G., Lesniak L., Zhang P. Graphs and Digraphs

3d ed. — Chapman and Hall/CRC Press, 1996. — 429 p. — ISBN 13 9780412987212.Graph theory is a major area of combinatorics, and during recent decades, graph theory has developed into a major area of mathematics. In addition to its growing interest and importance as a mathematical subject, it has applications to many fields, including computer science and chemistry. As in the first edition of Graphs & Digraphs (M. Behzad, G. Chartrand, L. Lesniak) and the second edition, our major, indeed our sole, objective is to introduce and to treat graph theory in the way we have always found it, namely, as the beautiful area of mathematics it is. We have strived to write a reader-friendly, carefully written book that emphasizes the mathematical theory of graphs and digraphs.
New to the third edition are expanded treatments of Hamiltonian graph theory, graph decompositions, and extremal graph theory, a study of graph vulnerability and domination in graphs; and introductions to voltage graphs, graph labelings, and the probabilistic method in graph theory. Numerous original exercises have been added. A comprehensive bibliography has been included together with an extensive list of graph theory books so that avid graph theory readers have many avenues to pursue their interests.
This text is intended for an introductory sequence in graph theory at the advanced undergraduate or beginning graduate level. A one-semester course can easily be designed by selecting those topics of major importance and interest to the instructor and students. Indeed, mathematical maturity is the only prerequisite for an understanding and an appreciation of the material presented.Introduction to graphs
Structure and symmetry of graphs
Trees and connectivity
Eulerian and Hamiltonian graphs and digraphs
Directed graphs
Planar graphs
Graph embeddings
Graph colorings
Matchings, factors and decompositions
Domination in graphs
Extremal graph theory
Ramsey theory
The probabilistic method in graph theory