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 (MSC 2000): 05C69
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