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In its second edition, expanded with new chapters on domination in graphs and on the spectral properties of graphs, this book offers a solid background in the basics of graph theory. Introduces such topics as Dirac´s theorem on k-connected graphs and more.

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This second edition includes two new chapters: one on domination in graphs and the other on the spectral properties of graphs, the latter including a discussion on graph energy. The chapter on graph colorings has been enlarged, covering additional topics such as homomorphisms and colorings and the uniqueness of the Mycielskian up to isomorphism.

This book also introduces several interesting topics such as Dirac´s theorem on k-connected graphs, Harary-Nashwilliam´s theorem on the hamiltonicity of line graphs, Toida-McKee´s characterization of Eulerian graphs, the Tutte matrix of a graph, Fournier´s proof of Kuratowski´s theorem on planar graphs, the proof of the nonhamiltonicity of the Tutte graph on 46 vertices, and a concrete application of triangulated graphs.

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Preface to the Second Edition.- Preface to the First Edition.- 1 Basic Results.- 2 Directed Graphs.- 3 Connectivity.- 4 Trees.- 5 Independent Sets and Matchings.- 6 Eulerian and Hamiltonian Graphs.- 7 Graph Colorings.- 8 Planarity.- 9 Triangulated Graphs.- 10 Domination in Graphs.- 11 Spectral Properties of Graphs.- Bibliography.- Index.

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From the reviews of the second edition:

"This book demonstrates the breadth of graph theory by including several explicit applications of graph theory to other disciplines. This could be used as a textbook for a graduate or undergraduate course. The streamlined text would make this a good reference book for an undergraduate or non-mathematician who uses graph theory. The embedded exercises make it a useful reference for a teacher of a graph theory course or a course in which selected topics of graph theory may occur." (Suzanne Caulk, MAA Reviews, June, 2013)
"The book goes from the basics to the frontiers of research in graph theory, with newly ideas emergent, in mathematics or computer science. ... Definitely the book is high recommended and is of much interest. It provides a solid background in the basic topics of graph theory, and is an excellent guide for graduate. I feel sure that it will be of great use to students, teachers and researchers." (Francisco José Cano Sevilla, The European Mathematical Society, April, 2013)

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