Abstract
<p>A set <em>D</em> - <em>V</em> is a dominating set of <em>G</em> if every vertex in <em>V - D</em> is adjacent to some vertex in <em>D</em>. The dominating number γ(<em>G</em>) of <em>G</em> is the minimum cardinality of a dominating set <em>D</em>. A dominating set <em>D</em> of a graph <em>G</em> = (<em>V;E</em>) is a split dominating set if the induced graph (<em>V</em> - <em>D</em>) is disconnected. The split domination number γ<em><sub>s</sub></em>(<em>G</em>) 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<br />obtained the exact values of γ<em>s</em>(<em>G<sub>m;n</sub></em>); <em>m</em> ≤ <em>n</em>; <em>m,n</em> ≤ 24:</p>
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