科研之友
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摘要
The Wiener index W of a connected graph G with vertex set V(G) is defined as W = Sigma(u,v is an element of V(G)) d(u, v) where d(u, v) stands for the distance between the vertices u and v of G. For S subset of V (G), the Steiner distance d(S) of the vertices of S is the minimum size of a connected subgraph of G whose vertex set contains S. The kth Steiner Wiener index SWk(G) of G is defined as the sum of Steiner distances of all k-element subsets of V (G). In 2005, Zhang and Wu studied the Nordhaus-Gaddum problem for the Wiener index. We now obtain analogous results for SWk, namely sharp upper and lower bounds for SWk(G)+SWk((G) over bar) and SWk(G). SWk(G), valid for any connected graph G whose complement G is also connected.
