The 2-rainbow domination number of Cartesian bundles over cycles

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

A k-rainbow dominating function (kRDF) of G assigns subsets of {1, 2, ..., k} to vertices, such that for vertex v with f(v) = ∅,▫$U_{u∈N(v)}$▫f(u) = {1, 2, ..., k}. The weight w(f) of kRDF f is w(f) =▫$\Sigma_{v∈V(G)}$▫|f(v)|. The minimum weight of a kRDF of G is the k-rainbow domination number denoted by ▫$\gamma_{rk}$▫(G). This paper focuses on the 2-rainbow domination number of Cartesian graph bundles of cycles over cycles, extending recent results for Cartesian product of cycles. Exact values are given for certain infinite families, and tight lower and upper bounds are established for general case.

• Language: English
• Keywords: 2-rainbow domination, domination numbers, graph bundles
• Work type: Article
• 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: Str. 641–659
• Numbering: Vol. 33
• PID: 20.500.12556/RUL-170865
• UDC: 519.17
• ISSN on article: 1613-9178
• DOI: 10.1007/s10100-024-00949-6
• COBISS.SI-ID: 216758531
• Publication date in RUL: 15.05.2026

Record is a part of a journal

• Title: Central European journal of operations research
• Shortened title: Cent. Eur. j. oper. res.
• Publisher: Springer Nature
• ISSN: 1613-9178
• COBISS.SI-ID: 513642521

Licences

• License: CC BY-NC-ND 4.0, Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International
• Link: http://creativecommons.org/licenses/by-nc-nd/4.0/
• Description: The most restrictive Creative Commons license. This only allows people to download and share the work for no commercial gain and for no other purposes.

Secondary language

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