The harmonic index of unicyclic graphs with given matching number

Jian Bo Lv, Jianxi Li*, Wai Chee SHIU

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

12 Citations (Scopus)

Abstract

The harmonic index of a graph G is defined as the sum of weights 2/d(u)+d(v) of all edges uv of G, where d(u) and d(v) are the degrees of the vertices u and v in G, respectively. In this paper, we determine the graph with minimum harmonic index among all unicyclic graphs with a perfect matching. Moreover, the graph with minimum harmonic index among all unicyclic graphs with a given matching number is also determined.

Original languageEnglish
Pages (from-to)173-183
Number of pages11
JournalKragujevac Journal of Mathematics
Volume38
Issue number1
DOIs
Publication statusPublished - Jun 2014

Scopus Subject Areas

  • Mathematics(all)

User-Defined Keywords

  • Harmonic index
  • Matching number
  • Unicyclic graph

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