steiner wiener index of graph products
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abstract
the wiener index $w(g)$ of a connected graph $g$ is defined as $w(g)=sum_{u,vin v(g)}d_g(u,v)$ where $d_g(u,v)$ is the distance between the vertices $u$ and $v$ of $g$. for $ssubseteq v(g)$, the {it 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 {it $k$-th steiner wiener index/} $sw_k(g)$ of $g$ is defined as $sw_k(g)=sum_{overset{ssubseteq v(g)}{|s|=k}} d(s)$. we establish expressions for the $k$-th steiner wiener index on the join, corona, cluster, lexicographical product, and cartesian product of graphs.
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Journal title:
transactions on combinatoricsPublisher: university of isfahan
ISSN 2251-8657
volume
issue Articles in Press 2016
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