A set S of vertices of a graph G is an independent dominating set of G if S is an independent set and every vertex not in S is adjacent to a vertex in S. The independent domination number of G, denoted by i(G), is the minimum cardinality of an independent dominating set of G. In this paper, some new classes of graphs with equal domination and independent domination numbers are presented and exa...

A subset of vertices in a graph G is total dominating set if every vertex adjacent to at least one this subset. The domination number the minimum cardinality any and denoted by ?t(G). having nonempty intersection with all independent sets maximum an transversal set. ?tt(G). Based on fact that for tree T, ?t(T) ? ?tt(T) + 1, work we give several relationships between trees T which are leading cl...

In this paper, we introduce the closed domination in graphs. Some interesting relationships are known between domination and closed domination and between closed domination and the independent domination. It is also shown that any triple m, k and n of positive integers with 3 ≤ m ≤ k ≤ n are realizable as the domination number, closed domination number and independent domination number, respect...