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
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