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.