Maximum graphs with a unique minimum dominating set

被引：5
|
作者：
Fischermann, M [1 ]
Rautenbach, D [1 ]
Volkmann, L [1 ]
机构：
[1] Rhein Westfal TH Aachen, Lehrstuhl Math 2, D-52056 Aachen, Germany
来源：
DISCRETE MATHEMATICS | 2003年 / 260卷 / 1-3期
关键词：
domination; size; unique minimum dominating set; extremal graphs;
D O I：
10.1016/S0012-365X(02)00670-2
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We present a conjecture on the maximum number of edges of a graph that has a unique minimum dominating set. We verify our conjecture for some special cases and prove a weakened version of this conjecture in general. (C) 2002 Elsevier Science B.V. All rights reserved.
引用
收藏
页码：197 / 203
页数：7
相关论文
共 50 条
  • [31] Maximum Number of Minimum Dominating and Minimum Total Dominating Sets
    Godbole, Anant
    Jamieson, Jessie D.
    Jamieson, William
    UTILITAS MATHEMATICA, 2014, 94 : 269 - 274
  • [32] On the complexity of the minimum outer-connected dominating set problem in graphs
    Pradhan, D.
    JOURNAL OF COMBINATORIAL OPTIMIZATION, 2016, 31 (01) : 1 - 12
  • [33] Brief Announcement: Local Approximability of Minimum Dominating Set on Planar Graphs
    Hilke, Miikka
    Lenzen, Christoph
    Suomela, Jukka
    PROCEEDINGS OF THE 2014 ACM SYMPOSIUM ON PRINCIPLES OF DISTRIBUTED COMPUTING (PODC'14), 2014, : 344 - 346
  • [34] Computing a minimum paired-dominating set in strongly orderable graphs
    Pradhan, D.
    Panda, B. S.
    DISCRETE APPLIED MATHEMATICS, 2019, 253 : 37 - 50
  • [35] An nO(1/ε) Approximation Scheme for the Minimum Dominating Set in Unit Disk Graphs
    Fakcharoephol, Jittat
    Sukprasert, Pattara
    2018 15TH INTERNATIONAL JOINT CONFERENCE ON COMPUTER SCIENCE AND SOFTWARE ENGINEERING (JCSSE), 2018, : 81 - 85
  • [36] An optimal algorithm for finding the minimum cardinality dominating set on permutation graphs
    Chao, HS
    Hsu, FR
    Lee, RCT
    DISCRETE APPLIED MATHEMATICS, 2000, 102 (03) : 159 - 173
  • [37] On the complexity of the minimum outer-connected dominating set problem in graphs
    D. Pradhan
    Journal of Combinatorial Optimization, 2016, 31 : 1 - 12
  • [38] An independent dominating set in the complement of a minimum dominating set of a tree
    Henning, Michael A.
    Loewenstein, Christian
    Rautenbach, Dieter
    APPLIED MATHEMATICS LETTERS, 2010, 23 (01) : 79 - 81
  • [39] Graphs with a unique maximum independent set up to automorphisms
    Bresar, Bostjan
    Dravec, Tanja
    Gorzkowska, Aleksandra
    Kleszcz, Elzbieta
    DISCRETE APPLIED MATHEMATICS, 2022, 317 : 124 - 135
  • [40] Minimum paired-dominating set in chordal bipartite graphs and perfect elimination bipartite graphs
    Panda, B. S.
    Pradhan, D.
    JOURNAL OF COMBINATORIAL OPTIMIZATION, 2013, 26 (04) : 770 - 785
12345