The harmonic index of a graph

Jianxi Li; Wai Chee Shiu

doi:10.1216/RMJ-2014-44-5-1607

The harmonic index of a graph

Jianxi Li, Wai Chee Shiu

Department of Mathematics

Research output: Contribution to journal › Journal article › peer-review

27 Citations (Scopus)

Abstract

The harmonic index of a graph G is defined as the sum of weights (Formula presented.) of all edges v_i v_j of G, where d(v_i) denotes the degree of the vertex v_i 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.

Original language	English
Pages (from-to)	1607-1620
Number of pages	14
Journal	Rocky Mountain Journal of Mathematics
Volume	44
Issue number	5
DOIs	https://doi.org/10.1216/RMJ-2014-44-5-1607
Publication status	Published - 2014

Scopus Subject Areas

General Mathematics

User-Defined Keywords

Bound
Effect
Graph
Harmonic index

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10.1216/RMJ-2014-44-5-1607

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The harmonic index of a graph

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