May 29, 2023
Doost Ali Mojdeh

Doost Ali Mojdeh

Degree: Professor
Address: Department of Mathematics, University of Mazandaran, Babolsar, Iran
Education: Ph.D in Mathematics (Graph Theory and Combinatorics)
Phone: 011-35302448
Faculty: Faculty of Mathematical Sciences


Title Rainbow domination in the Cartesian product of directed paths
Type Article
Rainbow domination, Cartesian product, directed graphs
Journal Australasian Journal of Combinatorics
Researchers Guoliang Hao (First researcher) , Doost Ali Mojdeh (Second researcher) , Souliu Wei (Third researcher) , Zhihong Xie (Fourth researcher)


For a positive integer k, a k-rainbow dominating function (kRDF) 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 with f(v) = ∅, u∈N(v), f(u) = {1, 2, . . . , k}, where N^{-}(v) is the set of in-neighbors of v. The weight of a kRDF f of D is the value v∈V (D), |f(v)|. The k-rainbow domination number of a digraph D, denoted by γrk(D), is the minimum weight of a kRDF of D. Let PmPn denote the Cartesian product of Pm and P_n, where Pm and Pn denote the directed paths of order m and n, respectively. In this paper, we determine the exact values of γrk(PmPn) for any positive integers k ≥ 2, m and n.