On the super domination number of graphs

The open neighborhood of a vertex v of a graph G is the set N (v) consisting of all vertices adjacent to v in G. For D subset of V (G), we define (D) over bar subset of V (G) \ D. A set D subset of V (G) is called a super dominating set of G if for every vertex u is an element of(D) over bar, there exists v is an element of D such that N (v) boolean AND (D) over bar = {u}. The super domination number of G is the minimum cardinality among all super dominating sets of G. In this paper, we obtain closed formulas and tight bounds for the super domination number of G in terms of several invariants of G. We also obtain results on the super domination number of corona product graphs and Cartesian product graphs.