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

页码：2141 / 2149

页数：9

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