New Bounds on the Double Total Domination Number of Graphs

Let G be a graph of minimum degree at least two. A set D subset of V(G) is said to be a double total dominating set of G if vertical bar N(v) boolean AND D vertical bar >= 2 for every vertex v epsilon V(G). The minimum cardinality among all double total dominating sets of G is the double total domination number of G. In this article, we continue with the study of this parameter. In particular, we provide new bounds on the double total domination number in terms of other domination parameters. Some of our results are tight bounds that improve some well-known results.