The Wiener Index and the Hosoya Polynomial of the Jahangir Graphs

TL;DR

This paper computes the Wiener index and Hosoya polynomial for Jahangir graphs J_5,m, providing new topological indices relevant for mathematical chemistry applications.

Contribution

It introduces explicit formulas for the Wiener index and Hosoya polynomial of Jahangir graphs J_5,m for all integers m ≥ 3.

Findings

Derived the Wiener index for Jahangir graphs J_5,m.

Calculated the Hosoya polynomial for Jahangir graphs J_5,m.

Enhanced understanding of topological indices in mathematical chemistry.

Abstract

Let G be a simple connected graph having vertex set V and edge set E. The vertex-set and edge-set of G denoted by V(G) and E(G), respectively. The length of the smallest path between two vertices is called the distance. Mathematical chemistry is the area of research engaged in new application of mathematics in chemistry. In mathematics chemistry, we have many topological indices for any molecular graph, that they are invariant on the graph automorphism. In this research paper, we computing the Wiener index and the Hosoya polynomial of the Jahangir graphs $J_5,m$ for all integer number $m \geq 3$.