On Wiener Polarity Index and Wiener Index of Certain Triangular Networks

Abstract

A topological index of graph $G$ is a numerical quantity which describes its topology. If it is applied to the molecular structure of chemical compounds, it reflects the theoretical properties of the chemical compounds. A number of topological indices have been introduced so far by different researchers. The Wiener index is one of the oldest molecular topological indices defined by Wiener. The Wiener index number reflects the index boiling points of alkane molecules. Quantitative structure activity relationships (QSAR) showed that they also describe other quantities including the parameters of its critical point, density, surface tension, viscosity of its liquid phase, and the van der Waals surface area of the molecule. The Wiener polarity index has been introduced by Wiener and known to be related to the cluster coefficient of networks. In this paper, the Wiener polarity index $W_p\left(G\right)$ and Wiener index $W\left(G\right)$ of certain triangular networks are computed by using graph-theoretic analysis, combinatorial computing, and vertex-dividing technology.