3-Tuple Total Domination Number of Rook's Graphs

Behnaz Pahlavsay; Elisa Palezzato; Michele Torielli

doi:10.7151/dmgt.2242

3-Tuple Total Domination Number of Rook's Graphs

Behnaz Pahlavsay, Elisa Palezzato, Michele Torielli

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

4 Scopus citations

Abstract

A k-tuple total dominating set (kTDS) of a graph G is a set S of vertices in which every vertex in G is adjacent to at least k vertices in S. The minimum size of a kTDS is called the k-tuple total dominating number and it is denoted by γ×k,t(G). We give a constructive proof of a general formula for γ×3,t(Kn□Km).

Original language	English (US)
Pages (from-to)	15-37
Number of pages	23
Journal	Discussiones Mathematicae - Graph Theory
Volume	42
Issue number	1
DOIs	https://doi.org/10.7151/dmgt.2242
State	Published - Feb 1 2022
Externally published	Yes

Keywords

Cartesian product of graphs
Vizing's conjecture
k-tuple total domination
rook's graph

ASJC Scopus subject areas

Discrete Mathematics and Combinatorics
Applied Mathematics

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AU - Palezzato, Elisa

AU - Torielli, Michele

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AB - A k-tuple total dominating set (kTDS) of a graph G is a set S of vertices in which every vertex in G is adjacent to at least k vertices in S. The minimum size of a kTDS is called the k-tuple total dominating number and it is denoted by γ×k,t(G). We give a constructive proof of a general formula for γ×3,t(Kn□Km).

KW - Cartesian product of graphs

KW - Vizing's conjecture

KW - k-tuple total domination

KW - rook's graph

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3-Tuple Total Domination Number of Rook's Graphs

Abstract

Keywords

ASJC Scopus subject areas

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