Signed total Roman k-domination in directed graphs
نویسندگان
چکیده
Let D be a finite and simple digraph with vertex set V (D). A signed total Roman k-dominating function (STRkDF) on D is a function f : V (D) → {−1, 1, 2} satisfying the conditions that (i) ∑ x∈N−(v) f(x) ≥ k for each v ∈ V (D), where N−(v) consists of all vertices of D from which arcs go into v, and (ii) every vertex u for which f(u) = −1 has an inner neighbor v for which f(v) = 2. The weight of an STRkDF f is ω(f) = ∑ v∈V (D) f(v). The signed total Roman k-domination number γk stR(D) of D is the minimum weight of an STRkDF on D. In this paper we initiate the study of the signed total Roman k-domination number of digraphs, and we present different bounds on γk stR(D). In addition, we determine the signed total Roman k-domination number of some classes of digraphs. Some of our results are extensions of known properties of the signed total Roman k-domination number γk stR(G) of graphs G.
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