# The Harary Index of a Graph

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

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

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

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

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.

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

- 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
- Print ISBN 978-3-662-45842-6
- Online ISBN 978-3-662-45843-3
- Series Print ISSN 2191-530X
- Series Online ISSN 2191-5318
- Buy this book on publisher's site