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Triple Roman domination in graphs

Author

Listed:
  • Abdollahzadeh Ahangar, H.
  • Álvarez, M.P.
  • Chellali, M.
  • Sheikholeslami, S.M.
  • Valenzuela-Tripodoro, J.C.

Abstract

The Roman domination in graphs is well-studied in graph theory. The topic is related to a defensive strategy problem in which the Roman legions are settled in some secure cities of the Roman Empire. The deployment of the legions around the Empire is designed in such a way that a sudden attack to any undefended city could be quelled by a legion from a strong neighbour. There is an additional condition: no legion can move if doing so leaves its base city defenceless. In this manuscript we start the study of a variant of Roman domination in graphs: the triple Roman domination. We consider that any city of the Roman Empire must be able to be defended by at least three legions. These legions should be either in the attacked city or in one of its neighbours. We determine various bounds on the triple Roman domination number for general graphs, and we give exact values for some graph families. Moreover, complexity results are also obtained.

Suggested Citation

  • Abdollahzadeh Ahangar, H. & Álvarez, M.P. & Chellali, M. & Sheikholeslami, S.M. & Valenzuela-Tripodoro, J.C., 2021. "Triple Roman domination in graphs," Applied Mathematics and Computation, Elsevier, vol. 391(C).
    • Handle: RePEc:eee:apmaco:v:391:y:2021:i:c:s0096300320304057
    DOI: 10.1016/j.amc.2020.125444
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    Cited by:

    1. Enrico Enriquez & Grace Estrada & Carmelita Loquias & Reuella J Bacalso & Lanndon Ocampo, 2021. "Domination in Fuzzy Directed Graphs," Mathematics, MDPI, vol. 9(17), pages 1-14, September.
    2. Peng Li, 2024. "The k-th Roman domination problem is polynomial on interval graphs," Journal of Combinatorial Optimization, Springer, vol. 48(3), pages 1-14, October.
    3. Abdollahzadeh Ahangar, H. & Chellali, M. & Sheikholeslami, S.M. & Valenzuela-Tripodoro, J.C., 2022. "Maximal double Roman domination in graphs," Applied Mathematics and Computation, Elsevier, vol. 414(C).
    4. Jia-Xiong Dan & Zhi-Bo Zhu & Xin-Kui Yang & Ru-Yi Li & Wei-Jie Zhao & Xiang-Jun Li, 2022. "The signed edge-domatic number of nearly cubic graphs," Journal of Combinatorial Optimization, Springer, vol. 44(1), pages 435-445, August.

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