On an open problem concerning total domination critical graphs

被引：11
|
作者：
Mojdeh, Doost Ali
Rad, Nader Jafari
机构：
[1] Univ Mazandaran, Dept Math, Babol Sar, Iran
[2] Inst Studies Theoret Phys & Math, Tehran, Iran
来源：
EXPOSITIONES MATHEMATICAE | 2007年 / 25卷 / 02期
关键词：
total domination; vertex critical; diameter;
D O I：
10.1016/j.exmath.2006.10.001
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
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 the total domination number of G. We call these graphs gamma(1)-critical. If such a graph G has total domination number k, we call it k-gamma(1)-critical. We verify an open problem of k-gamma(1)-critical graphs and obtain some results on the characterization of total domination critical graphs of order n = Delta(G)(gamma(1)(G) - 1) + 1. (c) 2006 Elsevier GmbH. All rights reserved.
引用
收藏
页码：175 / 179
页数：5
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