Algorithms for Computing Wiener Indices of Acyclic and Unicyclic Graphs

Abstract

Let $G=\left(V\left(G\right),E\left(G\right)\right)$ be a molecular graph, where $V\left(G\right)$ and $E\left(G\right)$ 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 $O\left(n\right)$ .