Vertex-edge domination in cubic graphs

被引：4
|
作者：
Ziemann, Radoslaw [1 ]
Zylinski, Pawel [1 ]
机构：
[1] Univ Gdansk, Fac Math Phys & Informat, PL-80308 Gdansk, Poland
来源：
DISCRETE MATHEMATICS | 2020年 / 343卷 / 11期
关键词：
vertex-edge domination; cubic graph; discharging method; linear programming; NUMBER;
D O I：
10.1016/j.disc.2020.112075
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We establish that any connected cubic graph of order n > 6 has a minimum vertex- edge dominating set of at most 10n/31 vertices, thus affirmatively answering the open question posed by Klostermeyer et al. in Discussiones Mathematicae Graph Theory, https://doi.org/10.7151/dmgt.2175. On the other hand, we present an infinite family of cubic graphs whose gamma(ve) ratio is equal to 2/7. Finally, we show that the problem of determining the minimum gamma(ve)-dominating set is NP-hard even in cubic planar graphs. (C) 2020 Elsevier B.V. All rights reserved.
引用
收藏
页数：14
相关论文
共 50 条
  • [31] On a Vertex-Edge Marking Game on Graphs
    Boštjan Brešar
    Nicolas Gastineau
    Tanja Gologranc
    Olivier Togni
    [J]. Annals of Combinatorics, 2021, 25 : 179 - 194
  • [32] On a Vertex-Edge Marking Game on Graphs
    Bresar, Bostjan
    Gastineau, Nicolas
    Gologranc, Tanja
    Togni, Olivier
    [J]. ANNALS OF COMBINATORICS, 2021, 25 (01) : 179 - 194
  • [33] Global vertex-edge domination chain and its characterization
    Chitra, S.
    Sattanathan, R.
    [J]. JOURNAL OF DISCRETE MATHEMATICAL SCIENCES & CRYPTOGRAPHY, 2012, 15 (4-5): : 259 - 268
  • [34] ON THE VERTEX-EDGE WIENER INDICES OF THORN GRAPHS
    Azari, Mahdieh
    [J]. MATEMATICKI VESNIK, 2019, 71 (03): : 263 - 276
  • [35] A Note on Vertex-Edge Wiener Indices of Graphs
    Azari, Mahdieh
    [J]. IRANIAN JOURNAL OF MATHEMATICAL CHEMISTRY, 2016, 7 (01): : 11 - 17
  • [36] On the dimer problem of the vertex-edge graph of a cubic graph
    Li, Shuli
    Li, Danyi
    Yan, Weigen
    [J]. DISCRETE MATHEMATICS, 2023, 346 (08)
  • [37] A lower bound on the total vertex-edge domination number of a tree
    Senthilkumar, B.
    Kumar, H. Naresh
    Venkatakrishnan, Y. B.
    [J]. DISCRETE MATHEMATICS ALGORITHMS AND APPLICATIONS, 2021, 13 (01)
  • [38] Algorithmic study on liar’s vertex-edge domination problem
    Bhattacharya, Debojyoti
    Paul, Subhabrata
    [J]. Journal of Combinatorial Optimization, 2024, 48 (03)
  • [39] Irregularity Measures of Subdivision Vertex-Edge Join of Graphs
    Zheng, Jialin
    Akhter, Shehnaz
    Iqbal, Zahid
    Shafiq, Muhammad Kashif
    Aslam, Adnan
    Ishaq, Muhammad
    Aamir, Muhammad
    [J]. JOURNAL OF CHEMISTRY, 2021, 2021
  • [40] Graphs with unique minimum vertex-edge dominating sets
    Senthilkumar, B.
    Chellali, M.
    Naresh Kumar, H.
    Venkatakrishnan, Yanamandram B.
    [J]. RAIRO-OPERATIONS RESEARCH, 2023, 57 (04) : 1785 - 1795
12345