Hyper- and reverse-Wiener indices of F-sums of graphs

The Wiener index W(G)=∑{u,v}⊂V(G)d(u,v)W(G)=∑{u,v}⊂V(G)d(u,v), the hyper-Wiener index WW(G)=12∑{u,v}⊂V(G)[d(u,v)+d2(u,v)] and the reverse-Wiener index Λ(G)=n(n−1)D2−W(G), where d(u,v)d(u,v) is the distance of two vertices u,vu,v in GG, d2(u,v)=d(u,v)2d2(u,v)=d(u,v)2, n=|V(G)|n=|V(G)| and DD is the diameter of GG. In [M. Eliasi, B. Taeri, Four new sums of graphs and their Wiener indices, Discrete Appl. Math. 157 (2009) 794–803], Eliasi and Taeri introduced the F-sums of two connected graphs. In this paper, we determine the hyper- and reverse-Wiener indices of the F-sum graphs and, subject to some condition, we present some exact expressions of the reverse-Wiener indices of the F-sum graphs.