Some distance-based topological indices of the strong product of a graph and a diameter two graph

The strong product G ⊠ H of simple graphs G and H has vertex set V(G)×V(H) and edge set {(u,x)(v,y) : uv ∈ E(G) and xy ∈ E(H), or uv ∈ E(G) and x=y,or u=v and xy ∈ E(H)}. For a connected graph G, the Wiener index W(G)=1/2 ∑_(u,v∈V(G)) d_G (u,v), the hyper-Wiener index WW(G)=1/2 W(G)+1/4 ∑_(u,v∈V(G)) (d_G (u,v))^2, and the Harary index H(G)=1/2 ∑_(u,v∈V(G)) 1/(d_G (u,v)). In this paper, for a connected graph G, we calculate the exact values of Wiener index, hyper-Wiener index and Harary index of G⊠H_0, where H_0 is a graph of diameter 2.