Remarks on Domination in Graphs

A graph G with no isolated vertex is total domination vertex critical if for any vertex V of G that is not adjacent to vertex of degree one the total domination number of G - V is less thanthe total domination number or G. We call these graphs total domination critical or just y- critical.If such a graph G has total domination number k, we call k- Y -critical. We study some resulys on the characterization of total domination critical graphs of order (G) +4.