Enumeration of Accurate Dominating Sets

Let g = (v; e) be a simple graph. a dominating set of g is a subset d ⊆ v such that every vertexnot in d is adjacent to at least one vertex in d. the cardinality of a smallest dominating set of g,denoted by γ(g), is the domination number of g. a dominating set d is a accurate dominating set of g,if no jdj-element subset of v n d is a dominating set of g. the accurate domination number, γa(g), isthe cardinality of a smallest accurate dominating set d. in this paper, after presenting preliminaries, wecount the number of accurate dominating sets of some specific graphs.