Abstract
An Italian dominating function on a digraph D with vertex set V(D) is defined as a function f:V(D)→{0,1,2} such that every vertex v∈V(D) with f(v)=0 has at least two in-neighbors assigned 1 under f or one in-neighbor w with f(w)=2. In this article, we determine the exact values of the Italian domination numbers of some products of directed cycles.
Highlights
Introduction and PreliminariesAn Italian dominating function (IDF) on a digraph D is defined as a function f : V ( D ) → {0, 1, 2}
Introduction and PreliminariesLet D = (V, A) be a finite simple digraph with vertex set V = V ( D ) and arc set A = A( D )
An Italian dominating function (IDF) on a digraph D is defined as a function f : V ( D ) → {0, 1, 2}
Summary
An Italian dominating function (IDF) on a digraph D is defined as a function f : V ( D ) → {0, 1, 2} Such that every vertex v ∈ V ( D ) with f (v) = 0 has at least two in-neighbors assigned 1 under f or one in-neighbor w with f (w) = 2. The Italian domination number of a digraph D, denoted by γ I ( D ), is the minimum taken over the weights of all Italian dominating functions on D. Mathematics 2020, 8, 1472 the author of [6] initiated the study of the Italian domination number in digraphs.
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