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Domatic Dot Stable Graphs

Author(s): Yamuna Manimuthu

Journal: Journal of Current Engineering Research
ISSN 2250-2637

Volume: 2;
Issue: 1;
Date: 2012;
Original page

Keywords: Domination | domatic number | domination dot stable | domatic dot stable

A set of vertices D in a graph G = ( V, E ) is a dominating set if every vertex of V ? D is adjacent to some vertex of D. A domatic partition of a graph G is a partition of V into disjoint sets V1, V2, ..., VK such that each Vi is a dominating set for G. The domatic number of G is maximum cardinality of a domatic partition of G and it is denoted by d ( G ). We define a graph G to be domatic dot stable ( dds ) if d ( G• uv ) = d ( G ) ? u, v ? V ( G ) such that u ? v. In this paper we have obtained conditions under which a given graph G is domatic dot stable and not domatic dot stable.
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