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Article overview
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Generalized power domination in WK-Pyramid Networks | | Seethu Varghese
; A. Vijayakumar
; | | Date: |
3 Aug 2015 | | Abstract: | The notion of power domination arises in the context of monitoring an
electric power system with as few phase measurement units as possible. The
$k-$power domination number of a graph $G$ is the minimum cardinality of a
$k-$power dominating set ($k-$PDS) of $G$. In this paper, we determine the
$k-$power domination number of WK-Pyramid networks, $WKP_{(C,L)}$, for all
positive values of $k$ except for $k=C-1, C geq 2$, for which we give an upper
bound. The $k-$propagation radius of a graph $G$ is the minimum number of
propagation steps needed to monitor the graph $G$ over all minimum $k-$PDS. We
obtain the $k-$propagation radius of $WKP_{(C,L)}$ in some cases. | | Source: | arXiv, 1508.0357 | | Services: | Forum | Review | PDF | Favorites | |
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