Infinite Families of Circular and Mobius Ladders that are Total Domination Game Critical

被引：5
|
作者：
Henning, Michael A. [1 ]
Klavzar, Sandi [2 ,3 ,4 ]
机构：
[1] Univ Johannesburg, Dept Pure & Appl Math, Johannesburg, South Africa
[2] Univ Ljubljana, Fac Math & Phys, Ljubljana, Slovenia
[3] Univ Maribor, Fac Nat Sci & Math, Maribor, Slovenia
[4] Inst Math Phys & Mech, Ljubljana, Slovenia
来源：
BULLETIN OF THE MALAYSIAN MATHEMATICAL SCIENCES SOCIETY | 2018年 / 41卷 / 04期
基金：
新加坡国家研究基金会;
关键词：
Total domination game; Game total domination number; Critical graph; Circular ladder; Mobius ladder; 3/5-CONJECTURE; 3/4-CONJECTURE; FORESTS; NUMBER;
D O I：
10.1007/s40840-018-0635-8
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Let .tg(G) denote the game total domination number of a graph G, and let G| v mean that a vertex v of G is declared to be already totally dominated. A graph G is total domination game critical if.tg(G| v) <.tg(G) holds for every vertex v in G. If.tg(G) = k, then G is further called k-.tg- critical. In this paper, we prove that the circular ladder C4k K2 is 4k-.tg- critical and that the Mobius ladder ML2k is 2k-.tg- critical.
引用
收藏
页码：2141 / 2149
页数：9
相关论文
共 50 条
  • [41] The game total domination problem is log-complete in PSPACE
    Bresar, Bostjan
    Henning, Michael A.
    INFORMATION PROCESSING LETTERS, 2017, 126 : 12 - 17
  • [42] Pendant Total Domination Polynomial of Some Families of Standard Graphs
    Rani, Jyoti
    Mehra, Seema
    COMMUNICATIONS IN MATHEMATICS AND APPLICATIONS, 2023, 14 (02): : 647 - 654
  • [43] Effect of vertex-removal on game total domination numbers
    Charoensitthichai, Karnchana
    Worawannotai, Chalermpong
    ASIAN-EUROPEAN JOURNAL OF MATHEMATICS, 2020, 13 (07)
  • [44] The 4/5 upper bound on the game total domination number
    Henning, Michael A.
    Klavzar, Sandi
    Rall, Douglas F.
    COMBINATORICA, 2017, 37 (02) : 223 - 251
  • [45] The 4/5 upper bound on the game total domination number
    Michael A. Henning
    Sandi Klavžar
    Douglas F. Rall
    Combinatorica, 2017, 37 : 223 - 251
  • [46] Maker-Breaker total domination game on cubic graphs
    Forcan, Jovana
    Mikalacki, Mirjana
    DISCRETE MATHEMATICS AND THEORETICAL COMPUTER SCIENCE, 2022, 24 (01):
  • [47] A PROOF OF THE 3/4-CONJECTURE FOR THE TOTAL DOMINATION GAME
    Portier, Julien
    Versteegen, Leo V.
    SIAM Journal on Discrete Mathematics, 2025, 39 (01) : 1 - 18
  • [48] A constructive characterization of total domination vertex critical graphs
    Wang, Chunxiang
    Hu, Zhiquan
    Li, Xiangwen
    DISCRETE MATHEMATICS, 2009, 309 (04) : 991 - 996
  • [49] A note on extremal total domination edge critical graphs
    Hanson, D
    Wang, P
    UTILITAS MATHEMATICA, 2003, 63 : 89 - 96
  • [50] On the Diameter of Total Domination Vertex-Critical Graphs
    Wang, Tao
    BULLETIN OF THE MALAYSIAN MATHEMATICAL SCIENCES SOCIETY, 2016, 39 : S193 - S203
12345