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⊆v(g), we define d=v(g)∖d. a set d⊆v(g) is called a super dominating set of g if for every vertex u∈d, there exists v∈d such that n(v)∩d={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.