Abstarct: Let G = (V, E) be a graph of order n. A set S ⊆ V (G) is a dominating set if every vertex in V is either in S or is adjacent to a vertex in S, that is, V (G) = N[S]. The domination number gamma(G) is the minimum cardinality of a dominating set of G, and a dominating set of minimum cardinality is called a gamma(G)-set A graph is vertex domination-critical if the removal of any vertex decreases its domination number, that is gamma(G − v) < gamma (G).