University of Isfahan Transactions on Combinatorics 2251-8657 5 3 2016 09 01 Steiner Wiener index of graph products 39 50 13499 10.22108/toc.2016.13499 EN Yaoping Mao Department of Mathematics, Qinghai Normal University Zhao Wang School of Mathematical Sciences, Beijing Normal Universit Ivan Gutman University of Kragujevac Kragujevac, Serbia Journal Article 2015 12 31 The Wiener index $W(G)$ of a connected graph $G$‎ ‎is defined as $W(G)=\sum_{u,v\in V(G)}d_G(u,v)$‎ ‎where $d_G(u,v)$ is the distance between the vertices $u$ and $v$ of‎ ‎$G$‎. ‎For $S\subseteq V(G)$‎, ‎the <em>Steiner distance</em> $d(S)$ of‎ ‎the vertices of $S$ is the minimum size of a connected subgraph of‎ ‎$G$ whose vertex set is $S$‎. ‎The  $k$-<em>th Steiner Wiener index</em>‎ ‎$SW_k(G)$ of $G$ is defined as‎ ‎$SW_k(G)=\sum_{\overset{S\subseteq V(G)}{|S|=k}} d(S)$‎. ‎We establish‎ ‎expressions for the $k$-th Steiner Wiener index on the join‎, ‎corona‎, ‎cluster‎, ‎lexicographical product‎, ‎and Cartesian product of graphs‎. https://toc.ui.ac.ir/article_13499_e8db28e08ac92c0269c208de9cd50572.pdf