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Pancyclic and Bipancyclic Graphs

  • John C. George
  • Abdollah Khodkar
  • W.D. Wallis

Part of the SpringerBriefs in Mathematics book series (BRIEFSMATH)

Table of contents

  1. Front Matter
    Pages i-xii
  2. John C. George, Abdollah Khodkar, W. D. Wallis
    Pages 1-7
  3. John C. George, Abdollah Khodkar, W. D. Wallis
    Pages 9-20
  4. John C. George, Abdollah Khodkar, W. D. Wallis
    Pages 21-34
  5. John C. George, Abdollah Khodkar, W. D. Wallis
    Pages 35-47
  6. John C. George, Abdollah Khodkar, W. D. Wallis
    Pages 49-67
  7. John C. George, Abdollah Khodkar, W. D. Wallis
    Pages 69-80
  8. John C. George, Abdollah Khodkar, W. D. Wallis
    Pages 81-97
  9. John C. George, Abdollah Khodkar, W. D. Wallis
    Pages 99-106
  10. Back Matter
    Pages 107-108

About this book

Introduction

This book is focused on pancyclic and bipancyclic graphs and is geared toward researchers and graduate students in graph theory. Readers should be familiar with the basic concepts of graph theory, the definitions of a graph and of a cycle. Pancyclic graphs contain cycles of all possible lengths from three up to the number of vertices in the graph. Bipartite graphs contain only cycles of even lengths, a bipancyclic graph is defined to be a bipartite graph with cycles of every even size from 4 vertices up to the number of vertices in the graph. Cutting edge research and fundamental results on pancyclic and bipartite graphs from a wide range of journal articles and conference proceedings are composed in this book to create a standalone presentation.

The following questions are highlighted through the book:

- What is the smallest possible number of edges in a pancyclic graph with v vertices?

- When do pancyclic graphs exist with exactly one cycle of every possible length?

- What is the smallest possible number of edges in a bipartite graph with v vertices?

- When do bipartite graphs exist with exactly one cycle of every possible length?

Keywords

pancyclic graph Bipancyclic Graph Minimal Pancyclicity Minimal Bipancyclicity Uniquely Pancyclic Graphs Graph Cycle directed graph undirected graph Hamiltonian graphs node-pancyclic vertex-pancyclic edge-pancyclic bipartite graph

Authors and affiliations

  • John C. George
    • 1
  • Abdollah Khodkar
    • 2
  • W.D. Wallis
    • 3
  1. 1.BARNESVILLEUSA
  2. 2.Department of MathematicsUniversity of West GeorgiaCarrolltonUSA
  3. 3.Department of MathematicsSouthern Illinois UniversityEvansvilleUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-31951-3
  • Copyright Information The Author(s) 2016
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-31950-6
  • Online ISBN 978-3-319-31951-3
  • Series Print ISSN 2191-8198
  • Series Online ISSN 2191-8201
  • Buy this book on publisher's site
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