CAJ | 학술논문

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G[D]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.
불함고립점적도G칭위전공제변림계적,여과대임의량개불상린정점u화v, 유γt(G+uv)<γt(G).야칭저양적도위γt-림계적. 여과해도G적전공제수위k,칭G위k-γt-림계적.일개γt-림계도G칭위강γt-림계적, 여과대임의정점v∈V(G)존재G적일개기수위γt(G)-1적공제집D사득G[D]제v외불함고립점.연구료강γt-림계도적성질,급출료일개유소적강γt-림계도구조대강γt-림계도적방법.
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 G[D] 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.