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Abstract
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Let D be a simple digraph with arc set A(D), and let j and k be two positive integers. A
function f : A(D) → {−1, 1} is said to be a signed star j-dominating function (SSjDF) on
D if Pa∈A(v) f(a) ≥ j for every vertex v of D, where A(v) is the set of arcs with head v.
A set {f1, f2, . . . , fd} of distinct SSjDFs on D with the property that Pd
i=1 fi(a) ≤ k for
each a ∈ A(D), is called a signed star (j, k)-dominating (SS(j, k)D) family (of functions)
on D. The maximum number of functions in a SS(j, k)D family on D is the signed star
(j, k)-domatic number of D, denoted by d(j,k)
SS (D). In this paper, we study properties
of the signed star (j, k)-domatic number of a digraph D. In particular, we determine
bounds on d(j,k)
SS (D). Some of our results extend these ones given by Sheikholeslami and
Volkmann [Signed star k-domination and k-domatic number of digraphs, submitted] for
the signed (j, 1)-domatic number.
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