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Steiner Wiener index of graph products | ||
| Transactions on Combinatorics | ||
| مقاله 58، دوره 5، شماره 3، آذر 2016، صفحه 39-50 اصل مقاله (251.57 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22108/toc.2016.13499 | ||
| نویسندگان | ||
| 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 | ||
| چکیده | ||
| 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. | ||
| کلیدواژه‌ها | ||
| Distance (in graph)؛ Steiner distance (in graph)؛ Steiner Wiener index؛ product (of graphs) | ||
| مراجع | ||
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