Steiner Wiener Index of Complete m−Ary Trees

Let G be a connected graph with vertex set V(G) and edge set E(G) For a subset S of V(G) the Steiner distance d(S) of S is the minimum size of a connected subgraph whose vertex set contains S. For an integer k with 2 ≤k ≤n − 1, the k-th Steiner Wiener index of a graph G is defined as SWk (G) = ∑S⊆V(G) d(S) |S|=k In this paper, we present exact values of the k -th Steiner Wiener index of complete m-ary trees by using inclusion-exclusion principle for various values of k.