Trees with unique Roman dominating functions of minimum weight
Mustapha Chellali, Nader Jafari Rad · Discrete Mathematics Algorithms and Applications · 2014
A Roman dominating function on a graph G is a function f : V(G) → {0, 1, 2} satisfying the condition that every vertex u of G for which f(u) = 0 is adjacent to at least one vertex v of G for which f(v) = 2. The weight of a Roman dominating function is the value f(V(G)) = ∑u∈V(G)f(u). In this paper we provide a constructive characterization of trees with unique Roman dominating functions of minimum weight.