20.500.12556/RUP-21999 The 2-rainbow domination number of Cartesian product of cycles 2-mavrično dominacijsko število kartezičnega produkta ciklov 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) = ∅ we have ⋃{u ∈ N(v)}f(u) = {1, 2, ..., k}. The weight w(f) of a kRDF f is defined as w(f) = ∑{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. 2-rainbow domination domination number Cartesian product 2-mavrična dominacija dominacijsko število kartezični produkt true false true Založba Univerze na Primorskem Angleški jezik Slovenski jezik Članek v reviji 2025-10-21 23:16:33 2025-10-21 23:16:33 2025-11-13 03:04:03 0000-00-00 00:00:00 2025 0 0 17 str. no. 3, [article no.] P3.04 Vol. 25 2025 0000-00-00 Zaloznikova Objavljeno NiDoloceno 0000-00-00 0000-00-00 2025-05-16 51 1855-3974 https://doi.org/10.26493/1855-3974.3168.74d AMC_Brezovnik,Rupnik_Poklukar,Zerovnik_2025.pdf AMC_Brezovnik,Rupnik_Poklukar,Zerovnik_2025.pdf 1 683BEF037D147D5502B23D0F7375D0A8 64e8c75a65990f07e5fccf6137ae4ad1a1f5e19611b794459d6e67ed54b24d09 e115014e-aec3-11f0-8f0b-005056ac49c0 https://repozitorij.upr.si/Dokument.php?lang=slv&id=31934 Založba Univerze na Primorskem 0 0 0