Extremum of the Vertex-Gutman Index of the Extended-Stars

Abstract

The Gutman index is a variant of the Wiener index, which is a graph parameter related to the degree and the distance. In this paper, we calculated the vertex-Gutman index of the extended-stars, studied the extremum of the vertex-Gutman index of the extended-stars. We obtained that, in the extended-stars, the vertex-Gutman index has the maximum at the center and has minimum at the vertices nearest the center.