 Triple Roman domination in graphsH. Abdollahzadeh Ahangar, M.P. Álvarez, M. Chellali, S.M. Sheikholeslami and J.C. Valenzuela-Tripodoro Applied Mathematics and Computation, 2021, vol. 391, issue 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. Keywords: Roman domination; Double Roman domination; Triple Roman domination (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:391:y:2021:i:c:s0096300320304057 DOI: 10.1016/j.amc.2020.125444 Access Statistics for this article Applied Mathematics and Computation is currently edited by Theodore Simos More articles in Applied Mathematics and Computation from Elsevier |
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