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On the Quasi-Total Roman Domination Number of Graphs

Author

Listed:
  • Abel Cabrera Martínez

    (Departament d’Enginyeria Informàtica i Matemàtiques, Universitat Rovira i Virgili, Av. Països Catalans 26, 43007 Tarragona, Spain)

  • Juan C. Hernández-Gómez

    (Facultad de Matemáticas, Universidad Autónoma de Guerrero, Carlos E. Adame No. 54, Col. Garita, Acapulco 39650, Mexico)

  • José M. Sigarreta

    (Facultad de Matemáticas, Universidad Autónoma de Guerrero, Carlos E. Adame No. 54, Col. Garita, Acapulco 39650, Mexico)

Abstract

Domination theory is a well-established topic in graph theory, as well as one of the most active research areas. Interest in this area is partly explained by its diversity of applications to real-world problems, such as facility location problems, computer and social networks, monitoring communication, coding theory, and algorithm design, among others. In the last two decades, the functions defined on graphs have attracted the attention of several researchers. The Roman-dominating functions and their variants are one of the main attractions. This paper is a contribution to the Roman domination theory in graphs. In particular, we provide some interesting properties and relationships between one of its variants: the quasi-total Roman domination in graphs.

Suggested Citation

  • Abel Cabrera Martínez & Juan C. Hernández-Gómez & José M. Sigarreta, 2021. "On the Quasi-Total Roman Domination Number of Graphs," Mathematics, MDPI, vol. 9(21), pages 1-11, November.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:21:p:2823-:d:673610
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    References listed on IDEAS

    as
    1. Chun-Hung Liu & Gerard J. Chang, 2013. "Roman domination on strongly chordal graphs," Journal of Combinatorial Optimization, Springer, vol. 26(3), pages 608-619, October.
    2. José M. Sigarreta, 2021. "Total Domination on Some Graph Operators," Mathematics, MDPI, vol. 9(3), pages 1-9, January.
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