The harmonic index of a graph

Jianxi Li, Wai Chee SHIU

Research output: Contribution to journalJournal articlepeer-review

27 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)1607-1620
Number of pages14
JournalRocky Mountain Journal of Mathematics
Issue number5
Publication statusPublished - 2014

Scopus Subject Areas

  • Mathematics(all)

User-Defined Keywords

  • Bound
  • Effect
  • Graph
  • Harmonic index


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