Cactus graphs with equal domination and complementary tree domination numbers

Let G = (V, E) be a graph without an isolated vertex. A set D subset of V(G) is a dominating set of G if every vertex of V(G) \ D has a neighbor in D. The domination number of G is the minimum cardinality of a dominating set of G, denoted by gamma(G). A complementary tree dominating set of a graph G is the set D of vertices of G such that D is a dominating set and the induced subgraph < V \ D > is a tree. The complementary tree domination number of a graph G, denoted by gamma(ctd)(G), is the minimum cardinality of a complementary tree dominating set of G. We characterize the class of cactus graphs for which gamma(ctd)(G) = gamma(G) and generalize the results in [4].