| Title: | Nut graphs with a prescribed number of vertex and edge orbits |
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| Authors: | ID Bašić, Nino (Author)
ID Damnjanović, Ivan (Author) |
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| Files: |  RAZ_Basic_Nino_2026.pdf (445,35 KB)
MD5: 88A373D5D6B2922A8B9EE3E1E3221868
 https://link.springer.com/article/10.1007/s10801-025-01492-6
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| Language: | English |
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| Work type: | Article |
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| Typology: | 1.01 - Original Scientific Article |
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| Organization: | FAMNIT - Faculty of Mathematics, Science and Information Technologies
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| Abstract: | A nut graph is a nontrivial graph whose adjacency matrix has a one-dimensional null space spanned by a vector without zero entries. Recently, it was shown that a nut graph has more edge orbits than vertex orbits. It was also shown that for any even $r \geq 2$ and any $k \geq r + 1$, there exist infinitely many nut graphs with r vertex orbits and k edge orbits. Here, we extend this result by finding all the pairs $(r, k)$ for which there exists a nut graph with $r$ vertex orbits and $k$ edge orbits. In particular, we show that for any $k \geq 2$, there are infinitely many Cayley nut graphs with $k$ edge orbits and $k$ arc orbits. |
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| Keywords: | nut graph, vertex orbit, edge orbit, arc orbit, Cayley graph, automorphism |
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| Publication version: | Version of Record |
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| Publication date: | 08.01.2026 |
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| Year of publishing: | 2026 |
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| Number of pages: | str. 1-12 |
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| Numbering: | Vol. 63, iss. 1, article no. 9 |
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| PID: | 20.500.12556/RUP-22449  |
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| UDC: | 519.17 |
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| ISSN on article: | 0925-9899 |
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| COBISS.SI-ID: | 264172035 |
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| Publication date in RUP: | 09.01.2026 |
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| Views: | 169 |
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| Downloads: | 5 |
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| Metadata: |    |
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