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

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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’ 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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Authors and Affiliations

  1. School of Mathematical Sciences, Universiti Sains Malaysia, USM Penang, 11800, Gelugor, Malaysia

    Noor A’lawiah Abd Aziz & Hailiza Kamarulhaili

  2. Department of Mathematics and Applied Mathematics, University of Johannesburg, Johannesburg, South Africa

    Michael A. Henning

  3. Department of Mathematics, Shahed University, Tehran, Iran

    Nader Jafari Rad

Authors
  1. Noor A’lawiah Abd Aziz
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  2. Michael A. Henning
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  3. Nader Jafari Rad
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  4. Hailiza Kamarulhaili
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Correspondence to Noor A’lawiah Abd Aziz.

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Abd Aziz, N.A., Henning, M.A., Rad, N.J. et al. Improved Bounds on the k-tuple (Roman) Domination Number of a Graph. Graphs and Combinatorics 38, 75 (2022). https://doi.org/10.1007/s00373-022-02471-5

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  • DOI: https://doi.org/10.1007/s00373-022-02471-5

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