Computing the split domination number of grid graphs - V. R. Girish; P. Usha (Indonesian Journal of Combinatorics, 2021)
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 γs(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 haveobtained the exact values of γs(Gm;n); m ≤ n; m,n ≤ 24: