Some results on the super domination number of a graph

Let G = (V, E) be a simple graph. A dominating set of G is a subset S subset of V such that every vertex not in S is adjacent to at least one vertex in S. The cardinality of a smallest dominating set of G, denoted by gamma(G), is the domination number of G. A dominating set S is called a super dominating set of G, if for every vertex u is an element of(S) over bar = V - S, there exists v is an element of S such that N(v) boolean AND (S) over bar = {u}. The cardinality of a smallest super dominating set of G, denoted by gamma sp(G), is the super domination number of G. In this paper, we study super domination number of some graph classes and present sharp bounds for some graph operations.