On rainbow domination of generalized Petersen graphs $P(ck, k)$

Žerovnik, Janez (author)

The structure of minimal weight rainbow domination functions of cubic graphs are studied. Based on general observations for cubic graphs, generalized Petersen graphs $P(ck, k)$ are characterized whose 4- and 5-rainbow domination numbers equal the general lower bounds. As $t$-rainbow domination of cubic graphs for $t$ ≥ 6 is trivial, characterizations of such generalized Petersen graphs $P(ck, k)$ are known for all $t$-rainbow domination numbers. In addition, new upper bounds for 4- and 5-rainbow domination numbers that are valid for all $P(ck, k)$ are provided.

• Language: English
• Keywords: graph domination, rainbow domination numbers, cubic graphs, 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: 2024
• Number of pages: Str. 440-448
• Numbering: Vol. 357
• PID: 20.500.12556/RUL-160508
• UDC: 519.17
• ISSN on article: 0166-218X
• DOI: 10.1016/j.dam.2024.07.052
• COBISS.SI-ID: 205519875
• Publication date in RUL: 29.08.2024

ŽEROVNIK, Janez, 2024, On rainbow domination of generalized Petersen graphs $P(ck, k)$. Discrete applied mathematics [online]. 2024. Vol. 357, p. 440–448. [Accessed 14 April 2025]. DOI 10.1016/j.dam.2024.07.052. Retrieved from: https://repozitorij.uni-lj.si/IzpisGradiva.php?lang=eng&id=160508

Record is a part of a journal

• Title: Discrete applied mathematics
• Shortened title: Discrete appl. math.
• Publisher: Elsevier
• ISSN: 0166-218X
• COBISS.SI-ID: 25342464

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 grafov, mavrična dominacija števil, kubični grafi, posplošeni Petersenovi grafi

Projects

• Funder: ARIS - Slovenian Research and Innovation Agency
• Project number: P2-0248
• Name: Inovativni izdelovalni sistemi in procesi