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A Textbook of Graph Theory

  • Textbook
  • © 2000

Overview

Authors:
  1. R. Balakrishnan

    1. Department of Mathematics, Bharathidasan University, Tiruchirappalli, Tamil Nadu, India

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  2. K. Ranganathan

    1. National College, Tiruchirappalli, Tamil Nadu, India

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    You can also search for this author in PubMed   Google Scholar

Part of the book series: Universitext (UTX)

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Table of contents (10 chapters)

  1. Front Matter

    Pages i-xi
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  2. Basic Results

    • R. Balakrishnan, K. Ranganathan
    Pages 1-32

  3. Directed Graphs

    • R. Balakrishnan, K. Ranganathan
    Pages 33-43

  4. Connectivity

    • R. Balakrishnan, K. Ranganathan
    Pages 44-66

  5. Trees

    • R. Balakrishnan, K. Ranganathan
    Pages 67-82

  6. Independent Sets and Matchings

    • R. Balakrishnan, K. Ranganathan
    Pages 83-101

  7. Eulerian and Hamiltonian Graphs

    • R. Balakrishnan, K. Ranganathan
    Pages 102-127

  8. Graph Colorings

    • R. Balakrishnan, K. Ranganathan
    Pages 128-151

  9. Planarity

    • R. Balakrishnan, K. Ranganathan
    Pages 152-184

  10. Triangulated Graphs

    • R. Balakrishnan, K. Ranganathan
    Pages 185-198

  11. Applications

    • R. Balakrishnan, K. Ranganathan
    Pages 199-211

  12. Back Matter

    Pages 213-228
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Keywords

About this book

Graph theory has experienced a tremendous growth during 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 book aims to provide a solid background in the basic topics of graph theory. It covers 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. The book does not presuppose deep knowledge of any branch of mathematics, but requires only the basics of mathematics. It can be used in an advanced undergraduate course or a beginning graduate course in graph theory.

Authors and Affiliations

  • Department of Mathematics, Bharathidasan University, Tiruchirappalli, Tamil Nadu, India

    R. Balakrishnan

  • National College, Tiruchirappalli, Tamil Nadu, India

    K. Ranganathan

About the authors

 

Bibliographic Information

  • Book Title: A Textbook of Graph Theory

  • Authors: R. Balakrishnan, K. Ranganathan

  • Series Title: Universitext

  • DOI: https://doi.org/10.1007/978-1-4419-8505-7

  • Publisher: Springer New York, NY

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer Science+Business Media New York 2000

  • eBook ISBN: 978-1-4419-8505-7Published: 11 November 2012

  • Series ISSN: 0172-5939

  • Series E-ISSN: 2191-6675

  • Edition Number: 1

  • Number of Pages: XI, 228

  • Topics: Combinatorics

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