Split domsaturation and Some New Parameters

Let G be any connected graph. The split domination number γs (G) of G is the minimum cardinality of a split dominating set. The split domsaturation number dss (G) of a graph G is the least positive integer k such that every vertex of G lies in a split dominating set of cardinality k. A split dominating set S ⊆ V (G) is said to be connected split dominating set if < S > is connected. The minimum cardinality of all connected split dominating sets of G is called the connected split omination number of G and is denoted by γcs (G). The uniform split domination number γus (G) of a graph G is the least positive integer k, such that every k-element split subset S of V is a dominating set in G. In this paper, we investigate several properties of these dominating sets.