The Wiener Polarity Index of Graph Products

Jing Ma1, Yongtang Shi1, Jun Yue1
1Center for Combinatorics and LPMC-TJKLC Nankai University, Tianjin 300071, China

Abstract

The Wiener polarity index of a graph \(G\), denoted by \(W_p(G)\), is the number of unordered pairs of vertices \(u, v\) such that the distance between \(u\) and \(v\) is three, introduced by Harold Wiener in 1947. This index is utilized to demonstrate quantitative structure-property relationships in various acyclic and cyclic hydrocarbons. In this paper, we investigate the Wiener polarity index on the Cartesian, direct, strong, and lexicographic products of two non-trivial connected graphs.