Orthogonalisability of joins of graphs
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| Název: | Orthogonalisability of joins of graphs |
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| Autoři: | Rupert H. Levene, Polona Oblak, Helena Šmigoc |
| Zdroj: | Linear Algebra and its Applications. 723:162-181 |
| Publication Status: | Preprint |
| Informace o vydavateli: | Elsevier BV, 2025. |
| Rok vydání: | 2025 |
| Témata: | Spectral Theory, Combinatorics, FOS: Mathematics, Combinatorics (math.CO), Spectral Theory (math.SP), 15B10, 15B57, 15A18, 05C50 |
| Popis: | A graph is said to be orthogonalisable if the set of real symmetric matrices whose off-diagonal pattern is prescribed by its edges contains an orthogonal matrix. We determine some necessary and some sufficient conditions on the sizes of the connected components of two graphs for their join to be orthogonalisable. In some cases, those conditions coincide, and we present several families of joins of graphs that are orthogonalisable. |
| Druh dokumentu: | Article |
| Jazyk: | English |
| ISSN: | 0024-3795 |
| DOI: | 10.1016/j.laa.2025.06.001 |
| DOI: | 10.48550/arxiv.2503.20582 |
| Přístupová URL adresa: | http://arxiv.org/abs/2503.20582 |
| Rights: | CC BY NC CC BY |
| Přístupové číslo: | edsair.doi.dedup.....2a91564c5e2b20c18d401fee8a053d11 |
| Databáze: | OpenAIRE |
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Nájsť tento článok vo Web of Science | Abstrakt: | A graph is said to be orthogonalisable if the set of real symmetric matrices whose off-diagonal pattern is prescribed by its edges contains an orthogonal matrix. We determine some necessary and some sufficient conditions on the sizes of the connected components of two graphs for their join to be orthogonalisable. In some cases, those conditions coincide, and we present several families of joins of graphs that are orthogonalisable. |
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| ISSN: | 00243795 |
| DOI: | 10.1016/j.laa.2025.06.001 |