Steiner Wiener index of graph products

Document Type : Research Paper


1 Department of Mathematics, Qinghai Normal University

2 School of Mathematical Sciences, Beijing Normal Universit

3 University of Kragujevac Kragujevac, Serbia


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 Steiner distance $d(S)$ of‎ ‎the vertices of $S$ is the minimum size of a connected subgraph of‎ ‎$G$ whose vertex set is $S$‎. ‎The  $k$-th Steiner Wiener index‎ ‎$SW_k(G)$ 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.


Main Subjects

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Volume 5, Issue 3 - Serial Number 3
September 2016
Pages 39-50
  • Receive Date: 31 December 2015
  • Revise Date: 27 January 2016
  • Accept Date: 26 February 2016
  • Published Online: 01 September 2016