A subset S of vertices in a graph G is a global total dominating set, or just GTDS, if S is a total dominating set of both G and G. The global total domination number γgt(G) of G is the minimum cardinality of a GTDS of G. We present bounds for the global total domination number in graphs.

A set of vertices W a graph G is total k-dominating when every vertex has at least k neighbors in W. In recent article, Chiarelli et al. (2019) prove that can be computed O(n3k) time proper interval with n and m edges. this note we reduce the complexity to O(m) for k=2.