  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.
