Document Type

Journal Article

Department/Unit

Department of Mathematics

Title

The harmonic index of a graph

Language

English

Abstract

Copyright ©2014 Rocky Mountain Mathematics Consortium The harmonic index of a graph G is defined as the sum of weights (Formula presented.) of all edges vi vj of G, where d(vi) denotes the degree of the vertex vi in G. In this paper, we study how the harmonic index behaves when the graph is under perturbations. These results are used to provide a simpler method for determining the unicyclic graphs with maximum and minimum harmonic index among all unicyclic graphs, respectively. Moreover, a lower bound for harmonic index is also obtained.

Keywords

Bound, Effect, Graph, Harmonic index

Publication Date

2014

Source Publication Title

Rocky Mountain Journal of Mathematics

Volume

44

Issue

5

Start Page

1607

End Page

1620

Publisher

Rocky Mountain Mathematics Consortium

DOI

10.1216/RMJ-2014-44-5-1607

Link to Publisher's Edition

http://dx.doi.org/10.1216/RMJ-2014-44-5-1607

ISSN (print)

00357596

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