A vertex subset S of graph G is a total dominating set of G if every vertex of G is adjacent to a vertex in S. For a graph G with no isolated vertex, the total domination number of G, denoted by γt (G), is the minimum cardinality of a total dominating set. A total dominating set of cardinality γt (G) is called a γt (G)-set. A graph G with no isolated vertex is total domination vertex critical if for any vertex v of G that is not adjacent to a vertex of degree one, the total domination number of G-v is less than the total domination number of...
