A total dominating set of a graph G is a set D of vertices of G such that every vertex of G has a neighbor in D. A vertex of a graph is said to dominate itself and all of its neighbors. A double dominating set of a graph G is a set D of vertices of G such that every vertex of G is dominated by at least two vertices of D. The total (double, respectively) domination number of a graph G is the min...

A node in a graph G = (V,E) is said to dominate itself and all nodes adjacent to it. A set S C V is a dominating set for G if each node in V is dominated by some node in S and is a double dominating set for G if each node in V is dominated by at least two nodes in S. First we give a brief survey of Nordhaus-Gaddum results for several domination-related parameters. Then we present new inequaliti...