Triple Roman Domination Number of Circulant Graph

Roman domination is a famous topic in graph theory originated from a defense strategy of Ancient Rome. Roman legions are deployed in some important military areas so that any attack could be resisted by a local legion or a supported legion from an adjacent area with two legions. A legion cannot move from the area having one legion to other areas. Triple Roman domination is presented to provide every area triple protection with less than triple costs. To determine the triple Roman domination number of a graph is NP-complete. In this paper, we study the triple Roman domination number of the circulant graph C(n;{1,2}). We determine the triple Roman domination number of C(n;{1,2}) for any integer n ≥ 5.