| Title: | Orientable domination in product-like graphs |
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| Authors: | ID Anderson, Sarah (Author)
ID Brešar, Boštjan (Author)
ID Klavžar, Sandi (Author)
ID Kuenzel, Kirsti (Author)
ID Rall, Douglas F. (Author) |
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| Files: |  PDF - Presentation file, download (366,61 KB)
MD5: 75412643A755D775B048FFDBDD0F94D4
 URL - Source URL, visit https://www.sciencedirect.com/science/article/pii/S0166218X22004267
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| Language: | English |
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| Typology: | 1.01 - Original Scientific Article |
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| Organization: |  IMFM - Institute of Mathematics, Physics, and Mechanics
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| Abstract: | 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]. |
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| Keywords: | digraph, domination, orientable domination number, packing, graph product, corona graph |
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| Publication status: | Published |
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| Publication version: | Version of Record |
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| Publication date: | 01.02.2023 |
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| Year of publishing: | 2023 |
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| Number of pages: | str. 62-69 |
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| Numbering: | Vol. 326 |
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| PID: | 20.500.12556/DiRROS-18486  |
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| UDC: | 519.17 |
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| ISSN on article: | 0166-218X |
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| DOI: | 10.1016/j.dam.2022.11.003 |
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| COBISS.SI-ID: | 135012355 |
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| Note: |
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| Publication date in DiRROS: | 20.03.2024 |
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| Views: | 543 |
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| Downloads: | 176 |
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