Improved Bounds on the k-tuple (Roman) Domination Number of a Graph

Noor A’lawiah Abd Aziz; Michael A. Henning; Nader Jafari Rad; Hailiza Kamarulhaili

doi:10.1007/s00373-022-02471-5

Improved Bounds on the k-tuple (Roman) Domination Number of a Graph

Noor A’lawiah Abd Aziz, Michael A. Henning, Nader Jafari Rad, Hailiza Kamarulhaili

Mathematics and Applied Mathematics

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

2 Citations (Scopus)

Abstract

In Henning and Jafari Rad (Graphs Combin, 37: 325–336, 2021), several new probabilistic upper bounds are given on the k-tuple domination number, k-domination number, Roman domination number, and Roman k-domination number of a graph using the well-known Brooks’ Theorem for vertex coloring, improving all of previous given bounds for the above domination variants. In this paper, we use the well-known Turán’s Theorem, and give a slight improvement of all above given bounds.

Original language	English
Article number	75
Journal	Graphs and Combinatorics
Volume	38
Issue number	3
DOIs	https://doi.org/10.1007/s00373-022-02471-5
Publication status	Published - Jun 2022

Keywords

Roman domination
Roman k-tuple domination
Turán’s Theorem
k-domination
k-tuple domination

ASJC Scopus subject areas

Theoretical Computer Science
Discrete Mathematics and Combinatorics

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10.1007/s00373-022-02471-5

Cite this

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abstract = "In Henning and Jafari Rad (Graphs Combin, 37: 325–336, 2021), several new probabilistic upper bounds are given on the k-tuple domination number, k-domination number, Roman domination number, and Roman k-domination number of a graph using the well-known Brooks{\textquoteright} Theorem for vertex coloring, improving all of previous given bounds for the above domination variants. In this paper, we use the well-known Tur{\'a}n{\textquoteright}s Theorem, and give a slight improvement of all above given bounds.",

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AU - Rad, Nader Jafari

AU - Kamarulhaili, Hailiza

PY - 2022/6

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N2 - In Henning and Jafari Rad (Graphs Combin, 37: 325–336, 2021), several new probabilistic upper bounds are given on the k-tuple domination number, k-domination number, Roman domination number, and Roman k-domination number of a graph using the well-known Brooks’ Theorem for vertex coloring, improving all of previous given bounds for the above domination variants. In this paper, we use the well-known Turán’s Theorem, and give a slight improvement of all above given bounds.

AB - In Henning and Jafari Rad (Graphs Combin, 37: 325–336, 2021), several new probabilistic upper bounds are given on the k-tuple domination number, k-domination number, Roman domination number, and Roman k-domination number of a graph using the well-known Brooks’ Theorem for vertex coloring, improving all of previous given bounds for the above domination variants. In this paper, we use the well-known Turán’s Theorem, and give a slight improvement of all above given bounds.

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KW - Turán’s Theorem

KW - k-domination

KW - k-tuple domination

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Improved Bounds on the k-tuple (Roman) Domination Number of a Graph

Abstract

Keywords

ASJC Scopus subject areas

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