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Some Properties of Double Roman Domination

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  • Hong Yang
  • Xiaoqing Zhou

Abstract

A double Roman dominating function on a graph is a function satisfying the conditions that every vertex for which is adjacent to at least one vertex for which or two vertices and for which and every vertex for which is adjacent to at least one vertex for which . The weight of a double Roman dominating function is the value . The minimum weight of a double Roman dominating function on a graph is called the double Roman domination number of . A graph with is called a double Roman graph. In this paper, we study properties of double Roman domination in graphs. Moreover, we find a class of double Roman graphs and give characterizations of trees with for .

Suggested Citation

  • Hong Yang & Xiaoqing Zhou, 2020. "Some Properties of Double Roman Domination," Discrete Dynamics in Nature and Society, Hindawi, vol. 2020, pages 1-5, August.
    • Handle: RePEc:hin:jnddns:6481092
    DOI: 10.1155/2020/6481092
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    Cited by:

    1. Darja Rupnik Poklukar & Janez Žerovnik, 2023. "Double Roman Domination: A Survey," Mathematics, MDPI, vol. 11(2), pages 1-20, January.
    2. Zehui Shao & Rija Erveš & Huiqin Jiang & Aljoša Peperko & Pu Wu & Janez Žerovnik, 2021. "Double Roman Graphs in P (3 k , k )," Mathematics, MDPI, vol. 9(4), pages 1-18, February.

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