Contents

Ars Combinatoria

  • Research article

On the Merrifield-Simmons Index and Hosoya Index of Bicyclic Graphs with a Given Girth

Renbin Sun1, Zhongxun Zhu1, Liansheng Tan1
1College of Mathematics and Statistics, South Central University for Nationalities, Wuhan 430074, P.R. China; Computer Science Department, Central China Normal University, Wuhan 430079, PR China.
  • Published: 31/01/2012

Abstract

For a graph \(G\), the Merrifield-Simmons index \(i(G)\) and the Hosoya index \(z(G)\) are defined as the total number of independent sets and the total number of matchings of the graph \(G\), respectively. In this paper, we characterize the graphs with the maximal Merrifield-Simmons index and the minimal Hosoya index, respectively, among the bicyclic graphs on \(n\) vertices with a given girth \(g\).

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Citation
Renbin Sun, Zhongxun Zhu, Liansheng Tan. On the Merrifield-Simmons Index and Hosoya Index of Bicyclic Graphs with a Given Girth[J], Ars Combinatoria, Volume 103. 465-478. .