A map f : V → {0, 1, 2} is a Roman dominating function on a graph G = (V, E) if for every vertex v ∈ V with f(v) = 0, there exists a vertex u, adjacent to v, such that f(u) = 2. The weight of a Roman ...

Abstract.For two vertices 𝑢 and 𝑣 of a graph 𝐺, the set 𝐼[𝑢, 𝑣] consists of all vertices lying on some 𝑢 - 𝑣 geodesic in 𝐺. If 𝑆 is a set of vertices of 𝐺, then 𝐼[𝑆] is the union of all ...