Integer Linear Programming Formulations for Triple and Quadruple Roman Domination Problems

Roman domination is a well researched topic in graph theory. Recently two new variants of Roman domination, namely triple Roman domination and quadruple Roman domination problems have been introduced, to provide better defense strategies. However, triple Roman domination and quadruple Roman domination problems are NP-hard. In this paper, we have provided genetic algorithm for solving triple and quadruple Roman domination problems. Programming (ILP) formulations for triple Roman domination and quadruple Roman domination problems have been proposed. The proposed models are implemented using IBM CPLEX 22.1 optimization solvers and obtained results for random graphs generated using NetworkX Erdos-Renyi model.