# Article

 Title: Antidomatic number of a graph (English) Author: Zelinka, Bohdan Language: English Journal: Archivum Mathematicum ISSN: 0044-8753 (print) ISSN: 1212-5059 (online) Volume: 33 Issue: 2 Year: 1997 Pages: 191-195 Summary lang: English . Category: math . Summary: A subset $D$ of the vertex set $V(G)$ of a graph $G$ is called dominating in $G$, if for each $x\in V(G)-D$ there exists $y\in D$ adjacent to $x$. An antidomatic partition of $G$ is a partition of $V(G)$, none of whose classes is a dominating set in $G$. The minimum number of classes of an antidomatic partition of $G$ is the number $\bar{d} (G)$ of $G$. Its properties are studied. (English) Keyword: dominating set Keyword: antidomatic partition Keyword: antidomatic number MSC: 05C35 idZBL: Zbl 0909.05031 idMR: MR1478772 . Date available: 2008-06-06T21:33:19Z Last updated: 2012-05-10 Stable URL: http://hdl.handle.net/10338.dmlcz/107610 . Reference: [1] Cockayne, E. J., Redetniemi, S. T.: Towards a theory of domination in graphs.Networks 7(1977), 247–261. MR 0483788 Reference: [2] Zelinka, B.: Some numerical invariants of graphs.DrSc dissertation, Charles University, Prague 1988 (Czech). .

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