The Steiner k-Wiener Index of Cacti

Let G be a connected graph. The Steiner k-Wiener index SWk(G) of graph G is defined as SWk(G)=∑S⊆V(G),|S|=kdG(S), where dG(S) represents the minimum size of a connected subgraph of G that connects S. Using some graph operations, we obtain the minimum value and the second minimum value of the Steiner k-Wiener index for cacti with order n and t cycles, and we characterize the corresponding extremal graphs by exploiting structural symmetries.