Symmetry and distance topology of graphs

Suppose G is a graph and x, y ϵV(G). The length of a shortest path connecting x and y is denoted by d(x; y). The sum of all distances between pair of vertices is called the Wiener index W(G) of G [1]. The modified Wiener index ˆ W is a graph invariant related to distance and symmetry of the graph under consideration. This invariant is defiend as In this talk, we will report our recent results on this subject [2].