Varieties of Roman domination III

Roman domination was introduced in 2004 by Cockayne et al. (2004). If V ( G ) is the vertex set of a graph G , then a function f : V ( G ) → { 0,1,2 } is a Roman dominating function if every vertex u ∈ V ( G ) for which f ( u ) = 0 is adjacent to at least one vertex v for which f ( v ) = 2 . The Roman domination number of a graph G , denoted by γ R ( G ) , is the minimum weight of a Roman dominating function on G . In this work, we continue to survey what has been done on Roman domination. Mainly, we will present several variations of Roman dominating functions, which are not contained in the survey articles Chellali et al. (2020) [45, 47], and Chellali et al. (2021).