Independent rainbow domination numbers of generalized Petersen graphs P(n, 2) and P(n, 3)

Gabrovšek, Boštjan (author), Peperko, Aljoša (author), Žerovnik, Janez (author)

We obtain new results on independent 2- and 3-rainbow domination numbers of generalized Petersen graphs P(n, k) for certain values of n,k ∈ $\mathbb{N}$. By suitably adjusting and applying a well established technique of tropical algebra (path algebra) we obtain exact 2-independent rainbow domination numbers of generalized Petersen graphs P(n, 2) and P(n, 3) thus confirming a conjecture proposed by Shao et al. In addition, we compute exact 3-independent rainbow domination numbers of generalized Petersen graphs P(n, 2). The method used here is developed for rainbow domination and for Petersen graphs. However, with some natural modifications, the method used can be applied to other domination type invariants, and to many other classes of graphs including grids and tori.

• Language: English
• Keywords: independent rainbow domination, independent rainbow domination number, generalized Petersen graphs, tropical algebra, path algebra
• Work type: Article
• Typology: 1.01 - Original Scientific Article
• Organization: FS - Faculty of Mechanical Engineering
• Publication status: Published
• Publication version: Version of Record
• Year: 2020
• Number of pages: 13 str.
• Numbering: Vol. 8, iss. 6, art. 996
• PID: 20.500.12556/RUL-133672
• UDC: 519.17
• ISSN on article: 2227-7390
• DOI: 10.3390/math8060996
• COBISS.SI-ID: 20459011
• Publication date in RUL: 08.12.2021

Record is a part of a journal

• Title: Mathematics
• Shortened title: Mathematics
• Publisher: MDPI AG
• ISSN: 2227-7390
• COBISS.SI-ID: 523267865

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: 18.06.2020

Secondary language

• Language: Slovenian
• Keywords: neodvisna mavrična dominacija, neodvisno mavrično dominacijsko število, posplošeni Petersonovi grafi, tropska algebra, algebra poti