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Upper signed k-domination number

Keywords: Signed k-dominating function, mimimal signed k-dominating function, upper signed k-domination number, directed graph.

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Abstract:

Let k 3 1 be an integer and let D = (V, A) be a finite simple digraph in which dD-(v) 3 k - 1 for all v V. A function f V {-1,1} is called a signed k-dominating function (SkDF) if f(N-[v]) 3 k for each vertex v V. An SkDF f of a digraph D is minimal if there is no SkDF g 1 f such that g(v) £ f(v) for each v V. The maximum values of v V f(v), taken over all minimal signed k-dominating functions f, is called the upper signed k-domination number GkS(D). In this paper, we present a sharp upper bound for GkS(D).

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