On 2-rainbow domination number of generalized Petersen graphs P(5k, k)

Erveš, Rija (author), Žerovnik, Janez (author)

We obtain new results on 2-rainbow domination number of generalized Petersen graphs P(5k, k). In some cases (for some infinite families), exact values are established, and in all other cases lower and upper bounds are given. In particular, it is shown that, for k > 3, γ$_{r2}$(P(5k, k)) = 4k for k ≡ 2, 8 mod 10, γ$_{r2}$(P(5k, k)) = 4k + 1 for k ≡ 5, 9 mod 10, 4k + 1 ≤ γ$_{r2}$(P(5k, k)) ≤ 4k + 2 for k ≡ 1, 6, 7 mod 10, and 4k + 1 ≤ γ$_{r2}$(P(5k, k)) ≤ 4k + 3 for k ≡ 0, 3, 4 mod 10.

• Language: English
• Keywords: rainbow domination, rainbow domination number, generalized Petersen graphs
• Work type: Article
• Typology: 1.01 - Original Scientific Article
• Organization: FS - Faculty of Mechanical Engineering
• Publication status: Published
• Publication version: Version of Record
• Year: 2021
• Number of pages: 12 str.
• Numbering: Vol. 13, iss. 5, art. 809
• PID: 20.500.12556/RUL-134473
• UDC: 519.17
• ISSN on article: 2073-8994
• DOI: 10.3390/sym13050809
• COBISS.SI-ID: 63479043
• Publication date in RUL: 17.01.2022

Record is a part of a journal

• Title: Symmetry
• Shortened title: Symmetry
• Publisher: Molecular Diversity Preservation International
• ISSN: 2073-8994
• COBISS.SI-ID: 517592345

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.
• Licensing start date: 06.05.2021

Secondary language

• Language: Slovenian
• Keywords: teorija grafov, dominacija v grafih, mavrična dominacija, posplošeni Petersenovi grafi