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.