A note on graphs with large girth and small minus domination number

被引:1
|
作者
Lee, J [1 ]
Sohn, MY
Kim, HK
机构
[1] Yeungnam Univ, Kyongsan 712749, South Korea
[2] Changwon Natl Univ, Changwon 641773, South Korea
[3] Catholic Univ Taegu Hyosung, Kyongsan 713702, South Korea
关键词
minus domination number; covering graph;
D O I
10.1016/S0166-218X(98)00082-1
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
Dunbar et al. (1998) in Ref. [3] introduced the minus domination number gamma(-) (G) of a graph G and two open problems. In this paper, we show that for every negative integer k and positive integer m greater than or equal to 3, there exists a graph G with girth m and gamma(-) (G) less than or equal to k which is a positive answer for the open problem 2 in Ref. [3]. (C) 1999 Elsevier Science B.V. All rights reserved.
引用
收藏
页码:299 / 303
页数:5
相关论文
共 50 条
  • [1] A note on the minus edge domination number in graphs
    Sheikholeslami, S. M.
    [J]. ARS COMBINATORIA, 2013, 110 : 447 - 453
  • [2] Domination number of cubic graphs with large girth
    Kral', Daniel
    Skoda, Petr
    Volec, Jan
    [J]. JOURNAL OF GRAPH THEORY, 2012, 69 (02) : 131 - 142
  • [3] On the minus domination number of graphs
    Liu, HL
    Sun, L
    [J]. CZECHOSLOVAK MATHEMATICAL JOURNAL, 2004, 54 (04) : 883 - 887
  • [4] On the Minus Domination Number of Graphs
    Hailong Liu
    Liang Sun
    [J]. Czechoslovak Mathematical Journal, 2004, 54 : 883 - 887
  • [5] Note on domination and minus domination numbers in cubic graphs
    Chen, YJ
    Cheng, TCE
    Ng, CT
    Shan, EF
    [J]. APPLIED MATHEMATICS LETTERS, 2005, 18 (09) : 1062 - 1067
  • [6] Domination in Cubic Graphs of Large Girth
    Rautenbach, Dieter
    Reed, Bruce
    [J]. COMPUTATIONAL GEOMETRY AND GRAPH THEORY, 2008, 4535 : 186 - +
  • [7] A note on independent domination in graphs of girth 6
    Haviland, Julie
    [J]. AUSTRALASIAN JOURNAL OF COMBINATORICS, 2008, 42 : 171 - 175
  • [8] A note on independent domination in graphs of girth 5
    Haviland, Julie
    [J]. AUSTRALASIAN JOURNAL OF COMBINATORICS, 2008, 40 : 301 - 304
  • [9] Domination and total domination in cubic graphs of large girth
    Dantas, Simone
    Joos, Felix
    Loewenstein, Christian
    Machado, Deiwison S.
    Rautenbach, Dieter
    [J]. DISCRETE APPLIED MATHEMATICS, 2014, 174 : 128 - 132
  • [10] Graphs with small or large Roman {3}-domination number
    Ebrahimi, Nafiseh
    Ahangar, Hossein Abdollahzadeh
    Chellali, Mustapha
    Sheikholeslami, Seyed Mahmoud
    [J]. RAIRO-OPERATIONS RESEARCH, 2023, 57 (03) : 1195 - 1208