چكيده لاتين :
For a graph G and positive integers k and r, a function f : V (G) ----> {0, 1, 2} is a distance-k Roman r-dominating function if every vertex u for which f(u) = 0 is within distance k of at least r vertices v for which f(v) = 2. The weight of a distance-k Roman r-dominating function is the
sum of labels attributed to all vertices. The distance-k Roman r-domination number of a graph G, denoted by γ r (k,r) R (G), is the minimum weight of a distance-k Roman r-dominating function on G. We present probabilistic bounds for the distance-k Roman r-domination number of a graph
G, and then we study this parameter in random graphs
