On 2-domination and 2-rainbow domination of cylindrical graphs

Žerovnik, Janez (author)

Cylindrical graphs and torus grid graphs are naturally constructed from subgraphs of the infinite grid by certain identifications of boundary vertices. Considering various domination type problems, it is usually possible to find an optimal solution on the infinite grid. To the contrary, exact values of invariants for the cylindrical and torus grid graphs are typically only known for special subfamilies, and are in general hard to compute. The 2-domination and 2-rainbow domination of cylindrical graphs is studied, and some new formulae and improved bounds are reported. We also consider weak 2-domination and singleton rainbow domination.

• Language: English
• Keywords: 2-domination, weak 2-domination, singleton 2-rainbow domination, 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: 2025
• Number of pages: 12 str.
• Numbering: Vol. 44, iss. 5, art. 239
• PID: 20.500.12556/RUL-169460
• UDC: 51:621
• ISSN on article: 1807-0302
• DOI: 10.1007/s40314-025-03201-2
• COBISS.SI-ID: 237531395
• Publication date in RUL: 29.05.2025

Record is a part of a journal

• Title: Computational & applied mathematics
• Shortened title: Comput. appl. math.
• Publisher: Springer Nature, Sociedade Brasileira de Matemática Aplicada e Computacional
• ISSN: 1807-0302
• COBISS.SI-ID: 520491801

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: 2-dominacija, šibka 2-dominacija, singleton 2-mavrična dominacija, cilindrični grafi

Projects

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

• Funder: ARIS - Slovenian Research and Innovation Agency
• Project number: J1-4031
• Name: Računalniška knjižnica za zavozlane strukture in aplikacije