极大γ_t-临界图

On Maximumγ_t-Critical Graphs

如果对没有孤立点的图G的任何一个不相邻于一次点的点v,子图G-v的全控制数小于图G的全控制数,则称G是全控点临界的.这类图又被称为γ_t-临界的.进一步地,如此一个图的全控制数为k,则称它为k-γ_t-临界的.该文主要是给出一个满足n=△(G)(γ_t(G)-1)+1的图类的结构性的证明.

A graph G with no isolated vertex is total domination vertex critical if for any vertex v of G that is not adjacent to a vertex of degree one, the total domination number of G - v is less than that of G. These graphs are called γt-critical. If such a graph G has total domination number k, it is called k - γt-critical. In this paper, the authors give the structure proof of those graphs satisfying n = △（G）（γt （G） - 1） ＋ 1.