Geodesic
Induced-paired domatic numbers of graphs
Mathematica Bohemica, Tome 127 (2002) no. 4, pp. 591-596

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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 $$ of $G$ induced by $D$ is regular of degree 1, then $D$ is called an induced-paired dominating set in $G$. A partition of $V(G)$, each of whose classes is an induced-paired dominating set in $G$, is called an induced-paired domatic partition of $G$. The maximum number of classes of an induced-paired domatic partition of $G$ is the induced-paired domatic number $d_{\text{ip}}(G)$ of $G$. This paper studies its properties.
A subset $D$ of the vertex set $V(G)$ of a graph $G$ is called dominating in $G$, if each vertex of $G$ either is in $D$, or is adjacent to a vertex of $D$. If moreover the subgraph $$
DOI : 10.21136/MB.2002.133954
Classification : 05C35, 05C69
Keywords: dominating set; induced-paired dominating set; induced-paired domatic number 
Zelinka, Bohdan. Induced-paired domatic numbers of graphs. Mathematica Bohemica, Tome 127 (2002) no. 4, pp. 591-596. doi: 10.21136/MB.2002.133954
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