Journal of Prime Research in Mathematics

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:,,,


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.


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