Wiener Index of Intuitionistic Fuzzy Graphs with an Application to Transport Network Flow

Abstract

The Wiener index $\left(\mathcal{WI}\right)$ is one of the connectivity parameters used to know the biochemical and physicochemical properties of compounds depending upon their molecular structures. Intuitionistic fuzzy graphs $\left(\text{IFG}s\right)$ are a convenient tool to represent the objects and relations between them with two types of information using truth membership degree and falsity membership degree. This research work presents the concept of $\mathcal{WI}$ under the structure $\text{IFG}s$ , $IF$ trees, and $IF$ cycles. Some bounds on $\mathcal{WI}$ are investigated. The relationship between $\mathcal{WI}$ and connectivity index $\left(\mathcal{CI}\right)$ is also studied. In the end of this study, an application of the $\mathcal{WI}$ in transport network flow is proposed.