On the signed total domatic numbers of directed graphs
نویسنده
چکیده
Let D = (V,A) be a finite simple directed graph (shortly digraph) in which dD(v) ≥ 1 for all v ∈ V . A function f : V −→ {−1, 1} is called a signed total dominating function if ∑ u∈N−(v) f(u) ≥ 1 for each vertex v ∈ V . A set {f1, f2, . . . , fd} of signed total dominating functions on D with the property that ∑d i=1 fi(v) ≤ 1 for each v ∈ V (D), is called a signed total dominating family (of functions) on D. The maximum number of functions in a signed total dominating family on D is the signed total domatic number of D, denoted by dst(D). In this paper we present some bounds on the signed total domatic number and we determine the signed total domatic number of some classes of digraphs.
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