Some Aspects of the Wiener Index for Sun Graphs

TL;DR

This paper computes the Wiener and Wiener polarity indices for sun graphs, explores their relationships with other topological indices, and derives the Hosoya polynomial, contributing to graph theory and chemical graph analysis.

Contribution

It introduces explicit formulas for Wiener and Wiener polarity indices of sun graphs and relates them to other topological indices, along with deriving the Hosoya polynomial.

Findings

Wiener index for sun graphs is explicitly calculated.

Wiener polarity index for sun graphs is determined.

Hosoya polynomial for sun graphs is derived.

Abstract

The Wiener index $W(G)$ is the sum of distances of all pairs of vertices of the graph $G$. The Wiener polarity index $W_{p}(G)$ of a graph $G$ is the number of unordered pairs of vertices $u$ and $v$ of $G$ such that the distance $d_{G}(u,v)$ between $u$ and $v$ is $3$. In this paper the Wiener and the Wiener polarity indices of sun graphs are computed. A relationship between those indices with some other topological indices are presented. Finally, we find the Hosoya (Wiener) polynomial for sun graphs.