Computing the split domination number of grid graphs

A set D - V is a dominating set of G if every vertex in V - D is adjacent to some vertex in D . The dominating number γ( G ) of G is the minimum cardinality of a dominating set D . A dominating set D of a graph G = ( V;E ) is a split dominating set if the induced graph ( V - D ) is disconnected. The split domination number γ s ( G ) is the minimum cardinality of a split domination set. In this paper we have introduced a new method to obtain the split domination number of grid graphs by partitioning the vertex set in terms of star graphs and also we have obtained the exact values of γ s ( G m;n ); m ≤ n ; m,n ≤ 24: