A Textbook of Graph Theory

ISBN-13: 9781461445289 / Angielski / Miękka / 2012 / 292 str.

R Balakrishnan

Opis

 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.

Recenzje

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)

Spis treści

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.

O autorze

R. Balakrishnan is currently an Adjunct Professor of Mathematics at Bharathidasan University in India.

Blurb

Graph theory experienced a tremendous growth in the 20th century. One of the main reasons for this phenomenon is the applicability of graph theory in other disciplines such as physics, chemistry, psychology, sociology, and theoretical computer science. This textbook provides a solid background in the basic topics of graph theory, and is intended for an advanced undergraduate or beginning graduate course in graph theory.
 
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.