Authors:
New edition extensively revised and updated
Includes two new chapters, one on domination in graphs and another on spectral properties of graphs
Contains a discussion on graph energy, a topic of current interest in spectral graph theory
Part of the book series: Universitext (UTX)
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Table of contents (11 chapters)
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Front Matter
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Back Matter
About this book
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.
Keywords
- Eulerian and Hamiltonian graphs
- directed graphs
- domination in graphs
- energy of a graph
- graph colorings
- independent sets and matchings
- planarity
- spectral graph theory
- triangulated graphs
Reviews
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)Authors and Affiliations
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, Department of Mathematics, Bharathidasan University, Tiruchirappalli, India
R. Balakrishnan
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Tiruchirappalli, India
K. Ranganathan
About the authors
R. Balakrishnan is currently an Adjunct Professor of Mathematics at Bharathidasan University in India.
Bibliographic Information
Book Title: A Textbook of Graph Theory
Authors: R. Balakrishnan, K. Ranganathan
Series Title: Universitext
DOI: https://doi.org/10.1007/978-1-4614-4529-6
Publisher: Springer New York, NY
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Science+Business Media, LLC, part of Springer Nature 2012
Softcover ISBN: 978-1-4614-4528-9Published: 20 September 2012
eBook ISBN: 978-1-4614-4529-6Published: 20 September 2012
Series ISSN: 0172-5939
Series E-ISSN: 2191-6675
Edition Number: 2
Number of Pages: XIII, 292
Number of Illustrations: 204 b/w illustrations
Topics: Graph Theory