Paired domination in graphs: A survey and recent results

被引:0
作者
Desormeaux, Wyatt J. [1 ]
Henning, Michael A. [1 ]
机构
[1] Univ Johannesburg, Dept Math, ZA-2006 Auckland Pk, South Africa
基金
新加坡国家研究基金会;
关键词
Paired dominating set; paired domination number; matching number; FREE CUBIC GRAPHS; CLAW-FREE GRAPHS; PERMUTATION GRAPHS; TIME ALGORITHM; PLANAR GRAPHS; UPPER-BOUNDS; TREES; NUMBER; PARAMETERS; DIAMETER;
D O I
暂无
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
A set S of vertices in a graph G is a paired dominating set if every vertex of G is adjacent to a vertex in S and the subgraph induced by S contains a perfect matching (not necessarily as an induced subgraph). The minimum cardinality of a paired dominating set of G is the paired domination number of G. This paper presents a survey of selected results on paired domination through 2013.
引用
收藏
页码:101 / 166
页数:66
相关论文
共 95 条
[1]  
[Anonymous], 1968, USPEKHIMAT NAUK
[2]  
[Anonymous], 2013, REDIFF
[3]   Ratios of some domination parameters in graphs and claw-free graphs [J].
Blidia, Mostafa ;
Chellali, Mustapha ;
Favaron, Odile .
GRAPH THEORY IN PARIS: PROCEEDINGS OF A CONFERENCE IN MEMORY OF CALUDE BERGE, 2007, :61-+
[4]   Characterizations of trees with equal paired and double domination numbers [J].
Blidia, Mostafa ;
Chellali, Mustapha ;
Haynes, Teresa W. .
DISCRETE MATHEMATICS, 2006, 306 (16) :1840-1845
[5]   GRAPH-THEORETIC PARAMETERS CONCERNING DOMINATION, INDEPENDENCE, AND IRREDUNDANCE [J].
BOLLOBAS, B ;
COCKAYNE, EJ .
JOURNAL OF GRAPH THEORY, 1979, 3 (03) :241-249
[6]  
Bresar B, 2008, TAIWAN J MATH, V12, P213
[7]   Dominating direct products of graphs [J].
Bresar, Bostjan ;
Klavzar, Sandi ;
Rall, Douglas F. .
DISCRETE MATHEMATICS, 2007, 307 (13) :1636-1642
[8]  
Bresar B, 2007, UTILITAS MATHEMATICA, V73, P255
[9]   Vizing's conjecture: a survey and recent results [J].
Bresar, Bostjan ;
Dorbec, Paul ;
Goddard, Wayne ;
Hartnell, Bert L. ;
Henning, Michael A. ;
Klavzar, Sandi ;
Rall, Douglas F. .
JOURNAL OF GRAPH THEORY, 2012, 69 (01) :46-76
[10]   VERTEX DOMINATION CRITICAL GRAPHS [J].
BRIGHAM, RC ;
CHINN, PZ ;
DUTTON, RD .
NETWORKS, 1988, 18 (03) :173-179