强全控制边临界图(英文)  

Strongly total domination edge critical graphs

作　　者：江璠[1] 侯新民[1] 

机构地区：[1]中国科学技术大学数学系,安徽合肥230026

出　　处：《中国科学技术大学学报》2008年第9期1024-1029,共6页JUSTC

基　　金：NNSF of China(10671191,10701068)

摘　　要：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.A graph G with no isolated vertex is total domination edge critical if for any nonadjacent 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.

关 键 词：全控制 临界 强临界 

分 类 号：O157.6[理学—数学]