$k$-Tuple total domination and mycieleskian graphs

	$k$-Tuple total domination and mycieleskian graphs
Transactions on Combinatorics
مقاله 2، دوره 1، شماره 1، خرداد 2012، صفحه 7-13 اصل مقاله (415.37 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22108/toc.2012.333
نویسنده
Adel P. Kazemi^*
UMA (University of Mohaghegh Ardabili)
چکیده
‎Let $k$ be a positive integer‎. ‎A subset $S$ of $V(G)$ in a graph $G$‎ ‎is a $k$-tuple total dominating set of $G$ if every vertex of $G$‎ ‎has at least $k$ neighbors in $S$‎. ‎The $k$-tuple total domination‎ ‎number $\gamma _{\times k,t}(G)$ of $G$ is the minimum cardinality‎ ‎of a $k$-tuple total dominating set of $G$‎. ‎In this paper for a‎ ‎given graph $G$ with minimum degree at least $k$‎, ‎we find some sharp‎ ‎lower and upper bounds on the $k$-tuple total domination number of the $m$‎ -‎Mycieleskian graph $\mu _{m}(G)$ of $G$ in terms on $k$ and $\gamma‎ ‎_{\times k,t}(G)$‎. ‎Specially we give the sharp bounds $\gamma‎ ‎_{\times k,t}(G)+1$ and $\gamma _{\times k,t}(G)+k$ for $\gamma‎ ‎_{\times k,t}(\mu _1(G))$‎, ‎and characterize graphs with $\gamma‎ ‎_{\times k,t}(\mu _1(G))=\gamma _{\times k,t}(G)+1$‎.
کلیدواژه‌ها
$k$-tuple total dominating set؛ k-tuple total domination number؛ $m$-Mycieleskian graph

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