强全控制边临界图

不含孤立点的图G称为全控制边临界的,如果对任意两个不相邻顶点u和v, 有γt(G uv)<γt(G).也称这样的图为γt-临界的. 如果该图G的全控制数为k,称G为k-γt-临界的.一个γt-临界图G称为强γt-临界的, 如果对任意顶点v∈V(G)存在G的一个基数为γt(G)-1的控制集D使得GD]除v外不含孤立点.研究了强γt-临界图的性质,给出了一个由小的强γt-临界图构造大强γt-临界图的方法.

Strongly total domination edge critical graphs

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.