Orientable domination in product-like graphs

Anderson, Sarah (author), Brešar, Boštjan (author), Klavžar, Sandi (author), Kuenzel, Kirsti (author), Rall, Douglas F. (author)

The orientable domination number, ${\rm DOM}(G)$, of a graph $G$ is the largest domination number over all orientations of $G$. In this paper, ${\rm DOM}$ is studied on different product graphs and related graph operations. The orientable domination number of arbitrary corona products is determined, while sharp lower and upper bounds are proved for Cartesian and lexicographic products. A result of Chartrand et al. from 1996 is extended by establishing the values of ${\rm DOM}(K_{n_1,n_2,n_3})$ for arbitrary positive integers $n_1,n_2$ and $n_3$. While considering the orientable domination number of lexicographic product graphs, we answer in the negative a question concerning domination and packing numbers in acyclic digraphs posed in [Domination in digraphs and their direct and Cartesian products, J. Graph Theory 99 (2022) 359-377].

• Language: English
• Keywords: digraph, domination, orientable domination number, packing, graph product, corona graph
• 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: 01.02.2023
• Year: 2023
• Number of pages: Str. 62-69
• Numbering: Vol. 326
• PID: 20.500.12556/RUL-155109
• UDC: 519.17
• ISSN on article: 0166-218X
• DOI: 10.1016/j.dam.2022.11.003
• COBISS.SI-ID: 135012355
• Publication date in RUL: 20.03.2024

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: usmerjeni graf, dominacija, orientabilno dominantno število, pakiranje, grafovski produkt, korona