Abstract
The Steiner \(k\)-Wiener index \(SW_{k}(G)\) of a connected graph \(G\) is defined as \(SW_{k}(G)=\sum\limits_{\substack{S\subseteq V(G)} \atop {|S|=k}}d(S)\), where the \(d(S)\) is equal to the subtree minimum size among subtrees of \(G\) that connect
\(S\). A unicyclic graph is a connected graph with the same number of edges and vertices. In this paper, we study the lower and upper bounds of Steiner \(k\)-Wiener index of unicyclic graphs. In addition, we also obtain the second largest
Steiner \(k\)-Wiener index among all trees.
