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MATHEMATICA BOHEMICA, Vol. 133, No. 2, pp. 167-178 (2008)
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Domination with respect to nondegenerate

and hereditary properties

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Vladimir Samodivkin

* Vladimir Samodivkin*, Department of Mathematics, University of Architecture, Civil Engineering and Geodesy, Hristo Smirnenski 1 Blv., 1046 Sofia, Bulgaria, e-mail: ` vlsam\_fte@uacg.bg`

**Abstract:** For a graphical property $\mathcal P$ and a graph $G$, a subset $S$ of vertices of $G$ is a $\mathcal P$-set if the subgraph induced by $S$ has the property $\mathcal {P}$. The domination number with respect to the property $\mathcal {P}$, is the minimum cardinality of a dominating $\mathcal P$-set. In this paper we present results on changing and unchanging of the domination number with respect to the nondegenerate and hereditary properties when a graph is modified by adding an edge or deleting a vertex.

**Keywords:** domination, independent domination, acyclic domination, good vertex, bad vertex, fixed vertex, free vertex, hereditary graph property, induced-hereditary graph property, nondegenerate graph property, additive graph property

**Classification (MSC2000):** 05C69

**Full text of the article:**

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