Hyper-Wiener and Harary indices of graphs with cut edges

Abstract

The Wiener index is the sum of distances between all pairs of vertices of a connected graph, whereas the hyper-Wiener index is another distance-based molecular structure descriptor first introduced by Randic. The Harary index is defined as the sum of reciprocals of distances between all pairs of vertices of a connected graph. In this paper, we characterized resp. the minimal graph with respect to hyper-Wiener index and the maximal one with respect to Harary index among all the connected graphs of order n and with k cut edges.