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Abstract
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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.
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