A Textbook of Graph Theory

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Springer Science & Business Media, Sep 20, 2012 - Mathematics - 292 pages
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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.

 

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Contents

Chapter 1 Basic Results
1
Chapter 2 Directed Graphs
37
Chapter 3 Connectivity
48
Chapter 4 Trees
73
Chapter 5 Independent Sets and Matchings
96
Chapter 6 Eulerian and Hamiltonian Graphs
117
Chapter 7 Graph Colorings
143
Chapter 8 Planarity
175
Chapter 9 Triangulated Graphs
206
Chapter 10 Domination in Graphs
221
Chapter 11 Spectral Properties of Graphs
241
List of Symbols
274
References
279
Index
287
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About the author (2012)

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

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