The implementation of Hosoya index and Hosoya polynomial into some graphs related to cycles

Herolistra Baskoroputro\(^b\), FM Bhatti\(^{a,∗}\), Hafiz Muhammad Humza\(^a\), Alfi Y. Zakiyyah\(^b\)

\(^a\)Department of Mathematics, Riphah International University, Gulberg Campus, Lahore, Pakistan.

\(^b\)Department of Mathematics and Statistics, School of Computer Sciences, Bina Nusantara University, Jakarta, Indonesia

Correspondence should be addressed to: h.baskoroputro@binuas.ac.id, fmbhatti@riphah.edu.pk, hafizhumza96@gmail.com, alfi.zakiyyah@binus.edu

Copyright © 2024 Herolistra Baskoroputro, FM Bhatti, Hafiz Muhammad Humza, Alfi Y. Zakiyyah. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Published: Received: 05 April 2024 Accepted: 16 May 2024; Published Online: 05 June 2024.

Abstract

The Hosoya index counts the number of independent edge sets in a graph, that is the number of subsets of the edge set such that no two edges in the subset share a vertex. Moreover, the Hosoya index gives important details on a graph’s structural properties, including its connectivity. It has applications in a variety of fields, including computational biology, networking, and chemistry. In our article, we study Hosoya indiex of amalgamation of cycles and edge-amalgamation of cycles. Moreover, in this article we study the restricted Hosoya polynomial of amalgamation of cycles and we also give the general form of topological index.

Keywords:

Hosoya index, edge-amalgamation of cycles, amalgamation of cycles, Hosoya polynomials.