Strongly total domination edge critical graphs
Hou Xin-min · 2008
A graph G with no isolated vertex is total domination edge critical if for any non-adjacent pair of vertices u and v, γt(G+uv)γt(G). These graphs we call γt-critical. If such a graph G has total domination number k, we call it k-γt-critical. A γt-critical graph G is strongly γt-critical if for any v∈V(G) there is a dominating set D of G with cardinality γt(G)-1 such that v∈D and GD has no isolated vertex except for v. The properties of strongly γt-critical graphs were studied, and a method for constructing a strongly critical graph from smaller ones was presented.