**
MATHEMATICA BOHEMICA, Vol. 127, No. 4, pp. 591-596 (2002)
**

# Induced-paired domatic numbers of graphs

## Bohdan Zelinka

* 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 (MSC2000):** 05C69, 05C35

**Full text of the article:**

[Previous Article] [Next Article] [Contents of this Number]

*
© 2005 ELibM and
FIZ Karlsruhe / Zentralblatt MATH
for the EMIS Electronic Edition
*