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

The Wiener index W(G)[email protected]?"{"u","v"}"@?"V"("G")d(u,v), the hyper-Wiener index WW(G)[email protected]?"{"u","v"}"@?"V"("G")[d(u,v)+d^2(u,v)] and the reverse-Wiener index @L(G)=n(n-1)D2-W(G), where d(u,v) is the distance of two vertices u,v in G, d^2(u,v)=d(u,v)^2, n=|V(G)| and D is the diameter of G. 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.