Roman domination

Roman domination --- римское доминирование.

A Roman dominating function on a graph [math]\displaystyle{ G = (V,E) }[/math] is a function [math]\displaystyle{ f: V \rightarrow \{0,1,2\} }[/math] satisfying the condition that every vertex [math]\displaystyle{ u }[/math] for which [math]\displaystyle{ f(u) = 0 }[/math] is adjacent to at least one vertex [math]\displaystyle{ v }[/math] for which [math]\displaystyle{ f(v) = 2 }[/math]. The weight of a Roman dominating function is the value [math]\displaystyle{ f(V) = \sum_{u \in V} f(u) }[/math]. The minimum weight of a Roman dominating function on a graph [math]\displaystyle{ G }[/math] is called the Roman domination number of [math]\displaystyle{ G }[/math].