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Properly Colored Connectivity of Graphs

  • Book
  • © 2018

Overview

Authors:
  1. Xueliang Li

    1. Center for Combinatorics, Nankai University, Tianjin, China

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  2. Colton Magnant

    1. Department of Mathematics, Georgia Southern University, Statesboro, USA

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  3. Zhongmei Qin

    1. College of Science, Chang’an University, Xi’an, China

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  • Unifies up-to-date results and techniques used to study the proper connection number
  • Outlines varied approaches and advances to current open problems and conjectures
  • Features different applications of chromatic graph theory

Part of the book series: SpringerBriefs in Mathematics (BRIEFSMATH)

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Table of contents (12 chapters)

  1. Front Matter

    Pages i-viii
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  2. Introduction

    • Xueliang Li, Colton Magnant, Zhongmei Qin
    Pages 1-8

  3. General Results

    • Xueliang Li, Colton Magnant, Zhongmei Qin
    Pages 9-13

  4. Connectivity Conditions

    • Xueliang Li, Colton Magnant, Zhongmei Qin
    Pages 15-22

  5. Degree Conditions

    • Xueliang Li, Colton Magnant, Zhongmei Qin
    Pages 23-39

  6. Domination Conditions

    • Xueliang Li, Colton Magnant, Zhongmei Qin
    Pages 41-45

  7. Operations on Graphs

    • Xueliang Li, Colton Magnant, Zhongmei Qin
    Pages 47-61

  8. Random Graphs

    • Xueliang Li, Colton Magnant, Zhongmei Qin
    Pages 63-72

  9. Proper k-Connection and Strong Proper Connection

    • Xueliang Li, Colton Magnant, Zhongmei Qin
    Pages 73-84

  10. Proper Vertex Connection and Total Proper Connection

    • Xueliang Li, Colton Magnant, Zhongmei Qin
    Pages 85-95

  11. Directed Graphs

    • Xueliang Li, Colton Magnant, Zhongmei Qin
    Pages 97-102

  12. Other Generalizations

    • Xueliang Li, Colton Magnant, Zhongmei Qin
    Pages 103-135

  13. Computational Complexity

    • Xueliang Li, Colton Magnant, Zhongmei Qin
    Pages 137-138

  14. Back Matter

    Pages 139-145
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Keywords

About this book

A comprehensive survey of proper connection of graphs is discussed in this book with real world applications in computer science and network security. Beginning with a brief introduction, comprising relevant definitions and preliminary results, this book moves on to consider a variety of properties of graphs that imply bounds on the proper connection number. Detailed proofs of significant advancements toward open problems and conjectures are presented with complete references. 

Researchers and graduate students with an interest in graph connectivity and colorings will find this book useful as it builds upon fundamental definitions towards modern innovations, strategies, and techniques. The detailed presentation lends to use as an introduction to proper connection of graphs for new and advanced researchers, a solid book for a graduate level topics course, or as a reference for those interested in expanding and further developing research in the area.


Reviews

“The book consists of amazingly beautiful concepts and results which are perfect epitomes of structural analysis of graphs and rich with logic, precision and high degree of intuition. The book also opens up new dimensions for further investigations. The authors really deserve much appreciation for the preparation such an amazing book.” (Sudev Naduvath, zbMATH 1475.05002, 2022)

Authors and Affiliations

  • Center for Combinatorics, Nankai University, Tianjin, China

    Xueliang Li

  • Department of Mathematics, Georgia Southern University, Statesboro, USA

    Colton Magnant

  • College of Science, Chang’an University, Xi’an, China

    Zhongmei Qin

Bibliographic Information

  • Book Title: Properly Colored Connectivity of Graphs

  • Authors: Xueliang Li, Colton Magnant, Zhongmei Qin

  • Series Title: SpringerBriefs in Mathematics

  • DOI: https://doi.org/10.1007/978-3-319-89617-5

  • Publisher: Springer Cham

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: The Author(s), under exclusive licence to Springer International Publishing AG, part of Springer Nature 2018

  • Softcover ISBN: 978-3-319-89616-8Published: 24 May 2018

  • eBook ISBN: 978-3-319-89617-5Published: 14 May 2018

  • Series ISSN: 2191-8198

  • Series E-ISSN: 2191-8201

  • Edition Number: 1

  • Number of Pages: VIII, 145

  • Number of Illustrations: 34 b/w illustrations

  • Topics: Combinatorics, Graph Theory

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