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 ⊆ 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 γ (G) , is the domination number of G. A dominating set S is called a super dominating set of G , if for every vertex u ∈ S ¯ = V − S , there exists v ∈ S such that N (v) ∩ S ¯ = { u }. The cardinality of a smallest super dominating set of G , denoted by γ 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. [ABSTRACT FROM AUTHOR]