The hyper-Wiener index of bicyclic graphs

Abstract

Let G be a simple connected graph. The Wiener index W(G) is the sum of all distances between vertices of G, whereas the hyper-Wiener index WW(G) is defined as WW(G) = 1/2 ∑ u,v€V,.,v(G) (d(u, v)+ d²(u,v)), with the summation going over all pairs of vertices in G. In this paper, we determine the extremal bicyclic graphs of order n with maximal and minimal hyper-Wiener index.