The signed <Emphasis Type="Italic">k</Emphasis>-domination number of directed graphs |
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Authors: | Maryam Atapour Seyyed Mahmoud Sheikholeslami Rana Hajypory Lutz Volkmann |
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Institution: | 1.Department of Mathematics,Azarbaijan University of Tarbiat Moallem,Tabriz,I.R. Iran;2.Department of Mathematics,Islamic Azad University, Branches of Heris,Heris,I.R. Iran;3.Lehrstuhl II für Mathematik,RWTH-Aachen University,Aachen,Germany |
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Abstract: | Let k ≥ 1 be an integer, and let D = (V; A) be a finite simple digraph, for which d
D
− ≥ k − 1 for all v ɛ V. A function f: V → {−1; 1} is called a signed k-dominating function (SkDF) if f(N
−v]) ≥ k for each vertex v ɛ V. The weight w(f) of f is defined by $
\sum\nolimits_{v \in V} {f(v)}
$
\sum\nolimits_{v \in V} {f(v)}
. The signed k-domination number for a digraph D is γ
kS
(D) = min {w(f|f) is an SkDF of D. In this paper, we initiate the study of signed k-domination in digraphs. In particular, 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. Some of our results are
extensions of well-known lower bounds of the classical signed domination numbers of graphs and digraphs. |
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Keywords: | |
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