The hyper-Wiener index of the generalized hierarchical product of graphs

The hyper Wiener index of the connected graph GG is WW(G)=12∑{u,v}⊆V(G)(d(u,v)+d(u,v)2), where d(u,v)d(u,v) is the distance between the vertices uu and vv of GG. In this paper we compute the hyper-Wiener index of the generalized hierarchical product of two graphs and give some applications of this operation.