International Journal of Engineering and Technology

Let G be a bipartite graph. A X-dominating set D of X of G is a strong nonsplit X-dominating set of G if every vertex in X-D is X-adjacent to all other vertices in X-D. The strong nonsplit X-domination number of a graph G, denoted by is the minimum cardinality of a strong nonsplit X-dominating set. We find the bounds for strong nonsplit X-dominating set and give its bipartite version.