Exact Algorithms for Weak Roman Domination

We consider the Weak Roman Domination problem. Given an undirected graph G = (V,E), the aim is to find a weak roman domination function (wrd-function for short) of minimum cost, i.e. a function f: V → {0,1,2} such that every vertex v ∈ V is defended (i.e. there exists a neighbor u of v, possibly u = v, such that \(f(u) \geqslant 1\)) and for every vertex v ∈ V with f(v) = 0 there exists a neighbor u of v such that \(f(u) \geqslant 1\) and the function f u → v defined by: