Hosoya index of total graphs and semitotal graphs

Document Type : Original Article


1 Islamic Azad University

2 Golestan University


The Hosoya index $Z(G)$ of a graph $G$ is the total number of matchings in it. In this paper, the recursive formulas of the Hosoya index of semitotal graph $Q(G)$ and total graph $T(G)$ for certain graphs $G$ are obtained. Moreover, we obtain the bounds of the Hosoya index of semitotal and total graphs of a connected graph $G$.

Graphical Abstract

Hosoya index of total graphs and semitotal graphs


Main Subjects

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Volume 8, Issue 1
In memory of Prof. Ali Reza Ashrafi
June 2023
Pages 23-33
  • Receive Date: 25 January 2023
  • Revise Date: 04 February 2023
  • Accept Date: 15 February 2023
  • Publish Date: 01 March 2023