مشخصات پژوهش

Let G = (V,E) be a simple and finite graph with vertex set V (G), and let k ≥ 1 be an integer. A signed double Roman k-dominating function (SDRkDF) on a graph G is a function f : V (G) → {−1, 1, 2, 3} such that (i) every vertex v with f(v) = −1 is adjacent to at least two vertices assigned with 2 or to at least one vertex w with f(w) = 3, (ii) every vertex v with f(v) = 1 is adjacent to at least one vertex w with f(w) ≥ 2 and (iii)  u∈N[v] f(u) ≥ k holds for any vertex v. The weight of an SDRkDF f is  u∈V (G) f(u), and the minimum weight of an SDRkDF is the signed double Roman k-domination number γk sdR(G) of G. In this paper, we initiate the study of the signed double Roman k-domination number in graphs and we present lower and upper bounds for γk sdR(T). In addition we determine this parameter for some classes of graphs.