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The degree distance (DD), which is a weight version of the Wiener index,  defined for a connected graph G as vertex-degree-weighted sum of the  distances, that is, DD(G) = Σ{u,v}V(G)[dG(u)+dG(v)]d[u,v|G), where dG(u)  denotes the degree of a vertex u in G and d(u,v|G) denotes the distance  between two vertices u and v in G: In this paper, we establish two upper  bounds for the degree distances of four sums of two graphs in terms of other  indices of two individual graphs.

Two upper bounds for the degree distances of four sums of graphs