The k-Rainbow Domination and Domatic Numbers of Di-graphs.

SHEIKHOLESLAMI, S. M.; VOLKMANN, LUTZ

For a positive integer k, a k-rainbow dominating function of a digraph D is a function f from the vertex set V (D) to the set of all subsets of the set {1, 2, . . . , k} such that for any vertex v ϵ V (D) with f(v) = ϕ, the condition SuϵN-(v) f(u) = {1, 2, . . . , k} is fulfilled, where N-(v) is the set of in-neighbors of v. A set {f1, f2, . . . , fd} of k-rainbow dominating functions on D with the property that Σdi=1 ∣fi(v)∣ ≤ k for each v ϵ V (D), is called a k-rainbow dominating family (of functions) on D. The maximum number of functions in a k-rainbow dominating family on D is the k-rainbow domatic number of D, denoted by drk(D). In this paper we initiate the study of the k-rainbow domatic number in digraphs, and we present some bounds for drk(D).

RAINBOWS; GEOMETRIC vertices; DIRECTED graphs; FUNCTIONAL analysis; NEIGHBOR-joining (Biomathematics); MATHEMATICAL models

Kyungpook Mathematical Journal, 2016, Vol 56, Issue 1, p69

1225-6951

Academic Journal

10.5666/KMJ.2016.56.1.69