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

Nader Jafari Rad | N. Alawiah | M. Henning | H. Kamaruhali

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URL :   http://research.shahed.ac.ir/WSR/WebPages/Report/PaperView.aspx?PaperID=169871
Date :  2022/03/08
Publish in :    Graphs and Combinatorics

Link :  https://link.springer.com/article/10.1007/s00373-022-02471-5
Keywords :Roman

Abstract :

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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.