The Steiner k-Wiener index of graphs with given minimum degree

Let G be a connected graph. The Steiner distance d(S) of a set S of vertices is the minimum size of a connected subgraph of G containing all vertices of S. For k∈N, the Steiner k-Wiener index SW_k(G) is defined as ∑_Sd(S), where the sum is over all k-element subsets of the vertex set of G. The average Steiner k-distance μ_k(G) of G is defined as [Formula presented]. In this paper we prove upper bounds on the Steiner Wiener index and the average Steiner distance of graphs with given order n and minimum degree δ. Specifically we show that [Formula presented]. We improve this bound for triangle-free graphs to [Formula presented]. All bounds are best possible.