On singleton 3-rainbow domination of cylindrical graphs

Žerovnik, Janez (author)

Domination is among the most popular topics in graph theory, both due to its combinatorial appeal and a number of practical applications. Cylindrical graphs are Cartesian products of a path and a cycle. Usually, for some special subfamilies, natural constructions exist that give exact solutions. On the other hand, in general, exact values of invariants on cylindrical graphs are hard to compute. In this paper, tight lower and upper bounds for singleton three-rainbow domination are proven and a subfamily of cylindrical graphs is found for which exact values are provided. The results complement recent findings for singleton two- and four-rainbow domination.

• Language: English
• Keywords: graph theory, singleton rainbow domination, grid graphs, cylindrical 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: 2026
• Number of pages: 13 str.
• Numbering: Vol. 14, no. 16, art. 2917
• PID: 20.500.12556/RUL-185602
• UDC: 519.17
• ISSN on article: 2227-7390
• DOI: 10.3390/math14162917
• COBISS.SI-ID: 287586307
• Publication date in RUL: 12.08.2026

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.

Secondary language

• Language: Slovenian
• Keywords: teorija grafov, mavrična dominacija, mrežni grafi, cilindrični grafi