A Textbook of Graph Theory

  • R. Balakrishnan
  • K. Ranganathan

Part of the Universitext book series (UTX)

Table of contents

  1. Front Matter
    Pages i-xii
  2. R. Balakrishnan, K. Ranganathan
    Pages 1-35
  3. R. Balakrishnan, K. Ranganathan
    Pages 37-47
  4. R. Balakrishnan, K. Ranganathan
    Pages 49-71
  5. R. Balakrishnan, K. Ranganathan
    Pages 73-95
  6. R. Balakrishnan, K. Ranganathan
    Pages 97-115
  7. R. Balakrishnan, K. Ranganathan
    Pages 117-142
  8. R. Balakrishnan, K. Ranganathan
    Pages 143-174
  9. R. Balakrishnan, K. Ranganathan
    Pages 175-205
  10. R. Balakrishnan, K. Ranganathan
    Pages 207-220
  11. R. Balakrishnan, K. Ranganathan
    Pages 221-239
  12. R. Balakrishnan, K. Ranganathan
    Pages 241-273
  13. Back Matter
    Pages 275-292

About this book

Introduction

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.

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

Authors and affiliations

  • R. Balakrishnan
    • 1
  • K. Ranganathan
    • 2
  1. 1., Department of MathematicsBharathidasan UniversityTiruchirappalliIndia
  2. 2.TiruchirappalliIndia

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4614-4529-6
  • Copyright Information Springer Science+Business Media New York 2012
  • Publisher Name Springer, New York, NY
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-1-4614-4528-9
  • Online ISBN 978-1-4614-4529-6
  • Series Print ISSN 0172-5939
  • Series Online ISSN 2191-6675
  • About this book