A k-rainbow dominating function (kRDF) of G is a function that assigns subsets of {1, 2, ..., k} to the vertices of G such that for vertices v with f(v) = Ř we have Uu?N(v)f(u) = {1, 2, ..., k}. The weight w(f) of a kRDF f is defined as w(f) = P v?V(G)|f(v)|. The minimum weight of a kRDF of G is called the k-rainbow domination number of G, which is denoted by ?rk(G). In this paper, we study the 2-rainbow domination number of the Cartesian product of two cycles. Exact values are given for a number of infinite families and we prove lower and upper bounds for all other cases.

Rights

URN

URN:NBN:SI:doc-8F13HQCA

COBISSID

212017155

DOI

10.26493/1855-3974.3168.74d

Added

20.02.2026

Metadata

Citation

APA:

Brezovnik, Simon, Rupnik Poklukar, Darja, Žerovnik, Janez (2025). The 2-rainbow domination number of Cartesian product of cycles. Ars mathematica contemporanea, volume 25, issue 3, 17 str. URN:NBN:SI:doc-8F13HQCA from http://www.dlib.si

MLA:

Brezovnik, Simon, Rupnik Poklukar, Darja, Žerovnik, Janez. "The 2-rainbow domination number of Cartesian product of cycles." Ars mathematica contemporanea volume 25. issue 3 (2025) 17 str..
<http://www.dlib.si/?URN=URN:NBN:SI:doc-8F13HQCA>

Ars mathematica contemporanea
2008-
(Assembly record)