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

Michael A. Henning; Sandi Klavžar

doi:10.1007/s40840-018-0635-8

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

Michael A. Henning, Sandi Klavžar

Mathematics and Applied Mathematics

Research output: Contribution to journal › Article › peer-review

8 Citations (Scopus)

Abstract

Let γ_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 γ_tg(G| v) < γ_tg(G) holds for every vertex v in G. If γ_tg(G) = k, then G is further called k-γ_tg-critical. In this paper, we prove that the circular ladder C4k□K2 is 4k-γ_tg-critical and that the Möbius ladder ML ₂ _k is 2k-γ_tg-critical.

Original language	English
Pages (from-to)	2141-2149
Number of pages	9
Journal	Bulletin of the Malaysian Mathematical Sciences Society
Volume	41
Issue number	4
DOIs	https://doi.org/10.1007/s40840-018-0635-8
Publication status	Published - 1 Oct 2018

Keywords

Circular ladder
Critical graph
Game total domination number
Möbius ladder
Total domination game

ASJC Scopus subject areas

General Mathematics

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10.1007/s40840-018-0635-8

Cite this

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title = "Infinite Families of Circular and M{\"o}bius Ladders that are Total Domination Game Critical",

abstract = "Let γtg(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 γtg(G| v) < γtg(G) holds for every vertex v in G. If γtg(G) = k, then G is further called k-γtg-critical. In this paper, we prove that the circular ladder C4k□K2 is 4k-γtg-critical and that the M{\"o}bius ladder ML 2 k is 2k-γtg-critical.",

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AU - Klavžar, Sandi

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N2 - Let γtg(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 γtg(G| v) < γtg(G) holds for every vertex v in G. If γtg(G) = k, then G is further called k-γtg-critical. In this paper, we prove that the circular ladder C4k□K2 is 4k-γtg-critical and that the Möbius ladder ML 2 k is 2k-γtg-critical.

AB - Let γtg(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 γtg(G| v) < γtg(G) holds for every vertex v in G. If γtg(G) = k, then G is further called k-γtg-critical. In this paper, we prove that the circular ladder C4k□K2 is 4k-γtg-critical and that the Möbius ladder ML 2 k is 2k-γtg-critical.

KW - Circular ladder

KW - Critical graph

KW - Game total domination number

KW - Möbius ladder

KW - Total domination game

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JO - Bulletin of the Malaysian Mathematical Sciences Society

JF - Bulletin of the Malaysian Mathematical Sciences Society

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ER -

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

Abstract

Keywords

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