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© 2015

The Harary Index of a Graph

Book

Part of the SpringerBriefs in Applied Sciences and Technology book series (BRIEFSAPPLSCIENCES)

Also part of the SpringerBriefs in Mathematical Methods book sub series (BRIEFSMATHMETH)

Table of contents

  1. Front Matter
    Pages i-xv
  2. Kexiang Xu, Kinkar Ch. Das, Nenad Trinajstić
    Pages 1-11
  3. Kexiang Xu, Kinkar Ch. Das, Nenad Trinajstić
    Pages 13-26
  4. Kexiang Xu, Kinkar Ch. Das, Nenad Trinajstić
    Pages 27-34
  5. Kexiang Xu, Kinkar Ch. Das, Nenad Trinajstić
    Pages 35-54
  6. Kexiang Xu, Kinkar Ch. Das, Nenad Trinajstić
    Pages 55-68
  7. Kexiang Xu, Kinkar Ch. Das, Nenad Trinajstić
    Pages 69-74

About this book

Introduction

This is the first book to focus on the topological index, the Harary index, of a graph, including its mathematical properties, chemical applications and some related and attractive open problems. This book is dedicated to Professor Frank Harary (1921—2005), the grandmaster of graph theory and its applications. It has be written by experts in the field of graph theory and its applications. For a connected graph G, as an important distance-based topological index, the Harary index H(G) is defined as the sum of the reciprocals of the distance between any two unordered vertices of the graph G. In this book, the authors report on the newest results on the Harary index of a graph. These results mainly concern external graphs with respect to the Harary index; the relations to other topological indices; its properties and applications to pure graph theory and chemical graph theory; and two significant variants, i.e., additively and multiplicatively weighted Harary indices. In the last chapter, we present a number of open problems related to the Harary index. As such, the book will not only be of interest to graph researchers, but to mathematical chemists as well.

 

Keywords

Distance in Graph Harary index Mathematical Chemistry Structure-Property Modeling additively weighted Harary index multiplicatively weighted Harary index

Authors and affiliations

  1. 1.College of Science Department of MathematicsNanjing University of Aeronautics and AstronauticsNanjingChina
  2. 2.College of Science Department of MathematicsSungkyunkwan UniversityGyeonggi-doKorea, Republic of (South Korea)
  3. 3.Rugjer Boskovic InstituteZagrebCroatia

Bibliographic information

  • Book Title The Harary Index of a Graph
  • Authors Kexiang Xu
    Kinkar Ch. Das
    Nenad Trinajstić
  • Series Title SpringerBriefs in Applied Sciences and Technology
  • Series Abbreviated Title SpringerBriefs in Applied Sciences
  • DOI https://doi.org/10.1007/978-3-662-45843-3
  • Copyright Information The Author(s) 2015
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Mathematics and Statistics Mathematics and Statistics (R0)
  • Softcover ISBN 978-3-662-45842-6
  • eBook ISBN 978-3-662-45843-3
  • Series ISSN 2191-530X
  • Series E-ISSN 2191-5318
  • Edition Number 1
  • Number of Pages XV, 74
  • Number of Illustrations 35 b/w illustrations, 0 illustrations in colour
  • Topics Graph Theory
    Combinatorics
    Math. Applications in Chemistry
  • Buy this book on publisher's site

Reviews

“The main purpose of this book is to survey the main concepts and results related to the Harary index of a graph. … Each of these chapters end up with a list of references including books, surveys and the most significant papers related to the topic. This book is a gift for the budding researchers related to the subjects mathematics, chemistry and biological sciences.” (P. Titus, zbMATH, Vol. 1365.05005, 2017)