Properties of independent Roman domination in graphs.
M. Adabi, Ehsan Ebrahimi, Nader Jafari Rad, Morteza Moradi · Australas. J Comb. · 2012
A Roman dominating function on a graph G is a function f : V (G) → {0, 1, 2} satisfying the condition that every vertex u for which f(u) = 0 is adjacent to at least one vertex v for which f(v) = 2. The weight of a Roman dominating function is the value f(V (G)) = ∑ u∈V (G) f(u). The Roman domination number of G, γR(G), is the minimum weight of a Roman dominating function on G. In this paper, we study independent Roman domination in graphs and obtain some properties, bounds and characterizations for the independent Roman domination number of a graph.