A survey on Roman domination parameters in directed graphs

Abstract

Unlike undirected graphs where the concept of Roman domination has been studied very extensively over the past 15 years, Roman domination remains little studied in digraphs. However, the published works are quite varied and deal with different aspects of Roman domination, including for example, Roman bondage, Roman reinforcement, Roman dominating family of functions and the signed version of some Roman dominating functions. In this survey, we will explore some Roman domination related results on digraphs, some of which are extensions of well-known properties of the Roman domination parameters of undirected graphs.