Signed k-Domatic Numbers of Digraphs
Hamideh Aram, Maryam Atapour, Seyed Mahmoud Sheikholeslami, Lutz Volkmann · RWTH Publications (RWTH Aachen) · 2013
Let D be a finite and simple digraph with vertex set V(D), and let f : V(D)! f 1; 1g be a two-valued function. If k 1 is an integer and Âx2N (v) f(x) k for each v2V(D), where N (v) consists of v and all vertices of D from which arcs go into v, then f is a signed k-dominating function on D. A setff1; f2;:::; fdg of distinct signed k-dominating functions of D with the property that  d=1 fi(v) 1 for each v2 V(D), is called a signed k-dominating family (of functions) of D. The maximum number of functions in a signed k-dominating family of D is the signed k-domatic number of D, denoted by dkS(D). In this note we initiate the study of the signed k-domatic numbers of digraphs and present some sharp upper bounds for this parameter.