The total domination number 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 ).

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and Yeo, A. Total
Domination in Graphs. New York: Springer, 2013.