On cubic rainbow domination regular graphs

Kuzman, Boštjan (author)

A d-regular graph X is called d-rainbow domination regular or d-RDR, if its d-rainbow domination number γ$_{rd}$(X) attains the lower bound n/2 for d-regular graphs, where n is the number of vertices. In the paper, two combinatorial constructions to construct new d-RDR graphs from existing ones are described and two general criteria for a vertex-transitive d-regular graph to be d-RDR are proven. A list of vertex-transitive 3-RDR graphs of small orders is produced and their partial classification into families of generalized Petersen graphs, honeycomb-toroidal graphs and a specific family of Cayley graphs is given by investigating the girth and local cycle structure of these graphs.

• Language: English
• Keywords: rainbow domination regular graphs, generalized Petersen graphs, honeycomb toroidal graphs, cubic vertex-transitive graphs
• Work type: Article
• Typology: 1.01 - Original Scientific Article
• Organization: PEF - Faculty of Education
• Publication status: Published
• Publication version: Version of Record
• Year: 2025
• Number of pages: Str. 26-38
• Numbering: Vol. 373
• PID: 20.500.12556/RUL-168895
• UDC: 519.17
• ISSN on article: 1872-6771
• DOI: 10.1016/j.dam.2025.04.046
• COBISS.SI-ID: 234771971
• Publication date in RUL: 06.05.2025

Record is a part of a journal

• Title: Discrete applied mathematics
• Publisher: Elsevier
• ISSN: 1872-6771
• COBISS.SI-ID: 23141893

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: dominacija rednih grafov, posplošeni Petersenovi grafi, toroidni grafi medenih satov

Projects

• Funder: ARIS - Slovenian Research and Innovation Agency
• Project number: J1-50000
• Name: Hamiltonski cikli z rotacijsko simetrijo v povezanih točkovno tranzitivnih grafih

• Funder: ARIS - Slovenian Research and Innovation Agency
• Project number: J1-3001
• Name: Terwilligerjeva algebra grafa