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Upper signed k-domination number of directed graphs

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Author(s): H. Aram | S. M. Sheikholeslami | L. Volkmann

Journal: Acta Mathematica Universitatis Comenianae
ISSN 0862-9544

Volume: LXXXI;
Issue: 1;
Start page: 9;
Date: 2012;
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Keywords: Signed k-dominating function | mimimal signed k-dominating function | upper signed k-domination number | directed graph

ABSTRACT
Let k &#179 1 be an integer and let D = (V, A) be a finite simple digraph in which dD-(v) &#179 k - 1 for all v &#206 V. A function f: V &#174 {-1,1} is called a signed k-dominating function (SkDF) if f(N-[v])&#179 k for each vertex v &#206 V. An SkDF f of a digraph D is minimal if there is no SkDF g &#185 fsuch that g(v) &#163 f(v) for each v &#206 V. The maximum values of &#229v &#206 V f(v), taken over all minimal signed k-dominating functions f, is called the upper signed k-domination number &#71kS(D). In this paper, we present a sharp upper bound for &#71kS(D).
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