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Mao, Y., Wang, Z., Gutman, I. (2016). Steiner Wiener index of graph products. Transactions on Combinatorics, 5(3), 39-50. doi: 10.22108/toc.2016.13499
Yaoping Mao; Zhao Wang; Ivan Gutman. "Steiner Wiener index of graph products". Transactions on Combinatorics, 5, 3, 2016, 39-50. doi: 10.22108/toc.2016.13499
Mao, Y., Wang, Z., Gutman, I. (2016). 'Steiner Wiener index of graph products', Transactions on Combinatorics, 5(3), pp. 39-50. doi: 10.22108/toc.2016.13499
Mao, Y., Wang, Z., Gutman, I. Steiner Wiener index of graph products. Transactions on Combinatorics, 2016; 5(3): 39-50. doi: 10.22108/toc.2016.13499

Steiner Wiener index of graph products

Article 58, Volume 5, Issue 3, September 2016, Page 39-50  XML PDF (252 K)
Document Type: Research Paper
DOI: 10.22108/toc.2016.13499
Authors
Yaoping Mao 1; Zhao Wang2; Ivan Gutman3
1Department of Mathematics, Qinghai Normal University
2School of Mathematical Sciences, Beijing Normal Universit
3University of Kragujevac Kragujevac, Serbia
Abstract
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.
Keywords
‎Distance (in graph)‎; ‎Steiner distance (in graph)‎; ‎Steiner Wiener index‎; ‎product (of graphs)
Main Subjects
05C12 Distance in graphs; 05C75 Structural characterization of families of graphs
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