Bohdan Zelinka, Department of Applied Mathematics, Technical University of Liberec, Voronezska 13, 460 01 Liberec, Czech Republic, e-mail: bohdan.zelinka@vslib.cz
Abstract: A subset $D$ of the vertex set $V(G)$ of a graph $G$ is called dominating in $G$, if each vertex of $G$ either is in $D$, or is adjacent to a vertex of $D$. If moreover the subgraph $\<D\>$ of $G$ induced by $D$ is regular of degree 1, then $D$ is called an induced-paired dominating set in $G$. A partition of $V(G)$, each of whose classes is an induced-paired dominating set in $G$, is called an induced-paired domatic partition of $G$. The maximum number of classes of an induced-paired domatic partition of $G$ is the induced-paired domatic number $d_{\ip}(G)$ of $G$. This paper studies its properties.
Keywords: dominating set, induced-paired dominating set, induced-paired domatic number
Classification (MSC 2000): 05C69, 05C35
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