The total domination number γ_t of a graph is the size of a smallest total dominating set, where a total dominating set is a set of vertices of the graph such that all vertices (including those in the set itself) have a neighbor in the set. Total dominating numbers are defined only for graphs having no isolated vertex (plus the trivial case of the singleton graph K_1). For example, in the Petersen graph illustrated above, γ(P) = 3 since the set S = {1, 2, 9} is a minimum dominating set, while γ_t(P) = 4 since S^t = {4, 8, 9, 10} is a minimum total dominating set.

dominating set | domination number