On global domination critical graphs

被引:11
|
作者
Dutton, Ronald D. [1 ]
Brigham, Robert C. [1 ]
机构
[1] Univ Cent Florida, Dept Math, Orlando, FL 32816 USA
关键词
Domination; Global domination; Changing and unchanging;
D O I
10.1016/j.disc.2008.06.005
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
A dominating set of a graph G = (V, E) is a subset S subset of V such that every vertex not in S is adjacent to at least one vertex of S. The domination number of G is the cardinality of a smallest dominating set. The global domination number, gamma(g)(G), is the cardinality, of a smallest set S that is simultaneously a dominating set of both G and its complement (G) over bar. Graphs for which gamma(g)(G - e) > gamma(g)(G) for all edges e is an element of E are characterized, as are graphs for which gamma(e)(G - e) < gamma(e)(G) for all edges e is an element of E whenever <(G)over bar> is disconnected. Progress is reported in the latter case when (G) over bar is connected. Published by Elsevier B.V.
引用
收藏
页码:5894 / 5897
页数:4
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