The 2-rainbow domination number of Cartesian product of cycles

Brezovnik, Simon (author), Rupnik Poklukar, Darja (author), Žerovnik, Janez (author)

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 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.

• Language: English
• Keywords: 2-rainbow domination, domination number, cartesian product
• Typology: 1.01 - Original Scientific Article
• Organization: FS - Faculty of Mechanical Engineering
• Publication status: Published
• Publication version: Version of Record
• Year: 2025
• Number of pages: 17 str.
• Numbering: Vol. 25, no. 3
• PID: 20.500.12556/RUL-169434
• UDC: 519.17
• ISSN on article: 1855-3966
• DOI: 10.26493/1855-3974.3168.74d
• COBISS.SI-ID: 212017155
• Publication date in RUL: 28.05.2025

Record is a part of a journal

• Title: Ars mathematica contemporanea
• Publisher: Društvo matematikov, fizikov in astronomov, Društvo matematikov, fizikov in astronomov, Univerza na Primorskem, Fakulteta za matematiko, naravoslovje in informacijske tehnologije
• ISSN: 1855-3966
• COBISS.SI-ID: 239049984

Licences

• License: CC BY 4.0, Creative Commons Attribution 4.0 International
• Link: http://creativecommons.org/licenses/by/4.0/
• Description: This is the standard Creative Commons license that gives others maximum freedom to do what they want with the work as long as they credit the author.

Secondary language

• Language: Slovenian
• Keywords: 2-mavrična dominacija, dominacijsko število, kartezični produkt grafov