Signed Total K-domination Numbers of Directed Graphs
نویسندگان
چکیده
Let k ≥ 1 be an integer, and let D = (V, A) be a finite and simple digraph in which dD(v) ≥ k for all v ∈ V . A function f : V −→ {−1, 1} is called a signed total k-dominating function (STkDF) if f(N−(v)) ≥ k for each vertex v ∈ V . The weight w(f) of f is defined by w(f) = ∑ v∈V f(v). The signed total k-domination number for a digraph D is γ kS(D) = min{w(f) | f is a STkDF of D}. In this paper, we initiate the study of signed total k-domination in digraphs and we present some sharp lower bounds for γ kS(D) in terms of the order, the maximum and minimum outdegree and indegree and the chromatic number.
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