On Roman balanced domination of graphs.

Let G be a graph with vertex set V. A function f : V → { − 1 , 0 , 2 } is called a Roman balanced dominating function (RBDF) of G if ∑ u ∈ N G [ v ] f (u) = 0 for each vertex v ∈ V. The maximum (resp. minimum) Roman balanced domination number γ R b M (G) (resp. γ R b m (G)) is the maximum (resp. minimum) value of ∑ v ∈ V f (v) among all Roman balanced dominating functions f. A graph G is called R d -balanced if γ R b M (G) = γ R b m (G) = 0. In this paper, we obtain several upper and lower bounds on γ R b M (G) and γ R b m (G) and further determine several classes of R d -balanced graphs. [ABSTRACT FROM AUTHOR]