On the equality of domination number and 2-domination number

Gülnaz, Boruzanli Ekinci (author), Bujtás, Csilla (author)

The $2$-domination number $\gamma_2(G)$ of a graph $G$ is the minimum cardinality of a set $D \subseteq V(G)$ for which every vertex outside $D$ is adjacent to at least two vertices in $D$. Clearly, $\gamma_2(G)$ cannot be smaller than the domination number $\gamma(G)$. We consider a large class of graphs and characterize those members which satisfy $\gamma_2=\gamma$. For the general case, we prove that it is NP-hard to decide whether $\gamma_2=\gamma$ holds. We also give a necessary and sufficient condition for a graph to satisfy the equality hereditarily.

• Language: English
• Keywords: domination number, 2-domination number, hereditary property, computational complexity
• Work type: Article
• Typology: 1.01 - Original Scientific Article
• Organization: FMF - Faculty of Mathematics and Physics
• Publication status: Published
• Publication version: Version of Record
• Publication date: 01.01.2024
• Year: 2024
• Number of pages: Str. 383-406
• Numbering: Vol. 44, no. 1
• PID: 20.500.12556/RUL-163136
• UDC: 519.17
• ISSN on article: 1234-3099
• DOI: 10.7151/dmgt.2452
• COBISS.SI-ID: 117087491
• Publication date in RUL: 02.10.2024

GÜLNAZ, Boruzanli Ekinci and BUJTÁS, Csilla, 2024, On the equality of domination number and 2-domination number. Discussiones mathematicae : Graph theory [online]. 2024. Vol. 44, no. 1, p. 383–406. [Accessed 11 April 2025]. DOI 10.7151/dmgt.2452. Retrieved from: https://repozitorij.uni-lj.si/IzpisGradiva.php?lang=eng&id=163136

Record is a part of a journal

• Title: Discussiones mathematicae : Graph theory
• Shortened title: Discuss. Math., Graph Theory
• Publisher: Technical University Press
• ISSN: 1234-3099
• COBISS.SI-ID: 7487065

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.

Projects

• Funder: ARRS - Slovenian Research Agency
• Project number: N1-0108
• Name: Prenos naboja v grafovski dominaciji