Graphs with disjoint 2-dominating sets

被引：0
|
作者：
Henning, Michael A. [1 ]
Topp, Jerzy [2 ]
机构：
[1] Univ Johannesburg, Dept Math & Appl Math, ZA-2006 Auckland Pk, South Africa
[2] Univ Appl Sci, Inst Appl Informat, PL-82300 Elblag, Poland
来源：
AUSTRALASIAN JOURNAL OF COMBINATORICS | 2022年 / 83卷
关键词：
D O I：
暂无
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
A subset D subset of V (G) is a dominating set of a multigraph G if every vertex in V(G) \ D has a neighbor in D, while D is a 2-dominating set of G if every vertex belonging to V(G)\D is joined by at least two edges with a vertex or vertices in D. A graph G is a (2, 2)-dominated graph if it has a pair (D, D') of disjoint 2-dominating sets of vertices of G. In this paper we present two characterizations of minimal (2, 2)-dominated graphs.
引用
收藏
页码：163 / 172
页数：10
相关论文
共 50 条
  • [1] ON GRAPHS WITH DISJOINT DOMINATING AND 2-DOMINATING SETS
    Henning, Michael A.
    Rall, Douglas F.
    [J]. DISCUSSIONES MATHEMATICAE GRAPH THEORY, 2013, 33 (01) : 139 - 146
  • [2] Disjoint dominating and 2-dominating sets in graphs
    Miotk, Mateusz
    Topp, Jerzy
    Zylinski, Pawel
    [J]. DISCRETE OPTIMIZATION, 2020, 35
  • [3] Spanning Trees with Disjoint Dominating and 2-Dominating Sets
    Miotk, Mateusz
    Zylinski, Pawel
    [J]. DISCUSSIONES MATHEMATICAE GRAPH THEORY, 2022, 42 (01) : 299 - 308
  • [4] On Proper 2-Dominating Sets in Graphs
    Bednarz, Pawel
    Pirga, Mateusz
    [J]. SYMMETRY-BASEL, 2024, 16 (03):
  • [5] Minimum 2-dominating sets in regular graphs
    Hoppen, Carlos
    Mansan, Giovane
    [J]. Discrete Applied Mathematics, 2022, 323 : 268 - 285
  • [6] Minimum 2-dominating sets in regular graphs
    Hoppen, Carlos
    Mansan, Giovane
    [J]. DISCRETE APPLIED MATHEMATICS, 2022, 323 : 268 - 285
  • [7] OUTER-CONNECTED 2-DOMINATING SETS OF GRAPHS
    Canoy, Sergio R., Jr.
    Domoloan, Bernadette D.
    [J]. ADVANCES AND APPLICATIONS IN DISCRETE MATHEMATICS, 2019, 20 (01): : 25 - 36
  • [8] Disproof of two conjectures on proper 2-dominating sets in graphs
    Chellali, Mustapha
    Volkmann, Lutz
    [J]. COMMUNICATIONS IN COMBINATORICS AND OPTIMIZATION, 2024,
  • [9] Disjoint dominating and total dominating sets in graphs
    Henning, Michael A.
    Loewenstein, Christian
    Rautenbach, Dieter
    Southey, Justin
    [J]. DISCRETE APPLIED MATHEMATICS, 2010, 158 (15) : 1615 - 1623
  • [10] On 2-dominating kernels in graphs
    Wloch, Andrzej
    [J]. AUSTRALASIAN JOURNAL OF COMBINATORICS, 2012, 53 : 273 - 284
12345