The Wiener index of the kkth power of a graph

The kkth power of a graph GG, denoted by GkGk, is a graph with the same vertex set as GG such that two vertices are adjacent in GkGk if and only if their distance is at most kk in GG. The Wiener index is a distance-based topological index defined as the sum of distances between all pairs of vertices in a graph. In this note, we give the bounds on the Wiener index of the graph GkGk. The Nordhaus–Gaddum-type inequality for the Wiener index of the graph GkGk is also presented.