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Bounds on the $k$-tuple domatic number of a graph

In: Mathematica Slovaca, vol. 61, no. 6
Lutz Volkmann

Details:

Year, pages: 2011, 851 - 858
Keywords:
domination, $k$-tuple domination, $k$-tuple domatic number
About article:
Let $k$ be a positive integer, and let $G$ be a simple graph with vertex set $V(G)$. A vertex of a graph $G$ dominates itself and all vertices adjacent to it. A subset $S\subseteq V(G)$ is a $k$-tuple dominating set of $G$ if each vertex of $V(G)$ is dominated by at least $k$ vertices in $S$. The $k$-tuple domatic number of $G$ is the largest number of sets in a partition of $V(G)$ into $k$-tuple dominating sets. In this paper, we present a lower bound on the $k$-tuple domatic number, and we establish Nordhaus-Gaddum inequalities. Some of our results extends those for the classical domatic number.
How to cite:
ISO 690:
Volkmann, L. 2011. Bounds on the $k$-tuple domatic number of a graph. In Mathematica Slovaca, vol. 61, no.6, pp. 851-858. 0139-9918. DOI: https://doi.org/10.2478/s12175-011-0052-z

APA:
Volkmann, L. (2011). Bounds on the $k$-tuple domatic number of a graph. Mathematica Slovaca, 61(6), 851-858. 0139-9918. DOI: https://doi.org/10.2478/s12175-011-0052-z
About edition: