IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v9y2021i21p2823-d673610.html
   My bibliography  Save this article

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
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/9/21/2823/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/9/21/2823/
    Download Restriction: no
    ---><---

    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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Tian Liu & Chaoyi Wang & Ke Xu, 2015. "Large hypertree width for sparse random hypergraphs," Journal of Combinatorial Optimization, Springer, vol. 29(3), pages 531-540, April.
    2. J. Amjadi & S. M. Sheikholeslami & M. Soroudi, 2018. "Nordhaus–Gaddum bounds for total Roman domination," Journal of Combinatorial Optimization, Springer, vol. 35(1), pages 126-133, January.
    3. Abel Cabrera Martínez & Suitberto Cabrera García & Andrés Carrión García & Frank A. Hernández Mira, 2020. "Total Roman Domination Number of Rooted Product Graphs," Mathematics, MDPI, vol. 8(10), pages 1-13, October.
    4. Cai-Xia Wang & Yu Yang & Hong-Juan Wang & Shou-Jun Xu, 2021. "Roman {k}-domination in trees and complexity results for some classes of graphs," Journal of Combinatorial Optimization, Springer, vol. 42(1), pages 174-186, July.
    5. Abolfazl Poureidi & Nader Jafari Rad, 2020. "Algorithmic and complexity aspects of problems related to total Roman domination for graphs," Journal of Combinatorial Optimization, Springer, vol. 39(3), pages 747-763, April.
    6. Abel Cabrera Martínez & Dorota Kuziak & Iztok Peterin & Ismael G. Yero, 2020. "Dominating the Direct Product of Two Graphs through Total Roman Strategies," Mathematics, MDPI, vol. 8(9), pages 1-13, August.
    7. Ahlam Almulhim & Bana Al Subaiei & Saiful Rahman Mondal, 2024. "Survey on Roman {2}-Domination," Mathematics, MDPI, vol. 12(17), pages 1-20, September.
    8. Abel Cabrera Martínez & Suitberto Cabrera García & Andrés Carrión García, 2020. "Further Results on the Total Roman Domination in Graphs," Mathematics, MDPI, vol. 8(3), pages 1-8, March.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:9:y:2021:i:21:p:2823-:d:673610. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.