Secure domination critical graphs

被引：22
|
作者：
Grobler, P. J. P. [2 ]
Mynhardt, C. M. [1 ]
机构：
[1] Univ Victoria, Dept Math & Stat, Victoria, BC V8W 3R4, Canada
[2] Univ Stellenbosch, Dept Math Sci, ZA-7602 Matieland, South Africa
来源：
DISCRETE MATHEMATICS | 2009年 / 309卷 / 19期
基金：
加拿大自然科学与工程研究理事会;
关键词：
Secure domination; Protection of a graph; Edge-removal-critical graph; ER-critical graph; ROMAN-EMPIRE; PROTECTION; TREES;
D O I：
10.1016/j.disc.2008.05.050
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
A Secure dominating set X of a graph G is a dominating set with the property that each vertex u is an element of V-G - X is adjacent to a vertex nu is an element of X such that (X - {nu}) U {u} is dominating. The minimum cardinality of such a set is called the secure domination number, denoted by gamma(s)(G). We are interested in the effect of edge removal on gamma(s)(G), and characterize gamma(s) ER-critical graphs, i.e. graphs for which gamma(s)(G - e) > gamma(s)(G) for any edge e of G, bipartite gamma(s)-ER-critical graphs and gamma(s)-ER-critical trees. (C) 2008 Elsevier B.V. All rights reserved.
引用
收藏
页码：5820 / 5827
页数：8
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