The connectivity and wiener index of order graph in symmetric group / S. M. Kasim

Let G be a finite group and x is an element of G. Then, the order graph of a finite group denoted by OG, is a digraph and for any two distinct vertices x and y, there is an edge from x to y if and only if x divide y. The Wiener index is defined as the summation of distances between all pairs of vertices in a graph. It is one of the topological indices which can be used for analyzing intrinsic properties of molecule structure in chemistry. In this paper, the connectivity and Wiener index of OG are evaluated from the order graph of symmetric groups of degree up to10.