The 2-rainbow domination number of Cartesian product of cyclesBrezovnik, Simon (Avtor) Rupnik Poklukar, Darja (Avtor) Žerovnik, Janez (Avtor) 2-rainbow dominationdomination numbercartesian productA 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) = ∅ 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 γrk(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.Društvo matematikov, fizikov in astronomov, Društvo matematikov, fizikov in astronomov, Univerza na Primorskem, Fakulteta za matematiko, naravoslovje in informacijske tehnologije20252025-11-21 10:00:22Neznano24206UDK: 519.17ISSN pri članku: 1855-3966DOI: 10.26493/1855-3974.3168.74dCOBISS_ID: 212017155sl