No abstract

Let G = V G , E G be a molecular graph, where V G and E G are the sets of vertices (atoms) and edges (bonds). A topological index of a molecular graph is a numerical quantity which helps to predict the chemical/physical properties of the molecules. The Wiener, Wiener polarity, and the terminal Wiener indices are the distance-based topological indices. In this paper, we described a linear time algorithm (LTA) that computes the Wiener index for acyclic graphs and extended this algorithm for unicyclic graphs. The same algorithms are modified to compute the terminal Wiener index and the Wiener polarity index. All these algorithms compute the indices in time O n .

The Wiener index WI is one of the connectivity parameters used to know the biochemical and physicochemical properties of compounds depending upon their molecular structures. Intuitionistic fuzzy graphs IFG s 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 WI under the structure IFG s , I F trees, and I F cycles. Some bounds on WI are investigated. The relationship between WI and connectivity index CI is also studied. In the end of this study, an application of the WI in transport network flow is proposed.