RT journal article
T1 Triple Roman domination in graphs
A1 Abdollahzadeh Ahangar, H.
A1 Álvarez Ruiz, María del Pilar
A1 Chellali, M.
A1 Sheikholeslami, S.M.
A1 Valenzuela Tripodoro, Juan Carlos
A2 Estadística e Investigación Operativa
A2 Matemáticas
K1 Roman domination
K1 domination
K1 double Roman domination
K1 triple Roman domination
AB 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 on 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: 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.
PB Elsevier Inc.
SN 0096-3003
YR 2021
FD 2021-02-15
LK http://hdl.handle.net/10498/30712
UL http://hdl.handle.net/10498/30712
LA eng
DS Repositorio Institucional de la Universidad de Cádiz
RD 10-may-2026