| Title: | On cubic polycirculant nut graphs |
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| Authors: | ID Bašić, Nino (Author)
ID Damnjanović, Ivan (Author) |
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| Files: |  RAZ_Basic_Nino_2025.pdf (581,83 KB)
MD5: BF277F4DDD8652434F814319A5E120B7
 https://link.springer.com/article/10.1007/s40314-025-03218-7
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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 simple graph whose adjacency matrix contains a one-dimensional null space spanned by a vector without zero entries. Moreover, an $\ell$-circulant graph is a graph that admits a cyclic group of automorphisms having $\ell$ vertex orbits of equal size. It is not difficult to observe that there exists no cubic $1$-circulant nut graph or cubic $2$-circulant nut graph, while the full classification of all the cubic $3$-circulant nut graphs was recently obtained (Damnjanović et al. in Electron. J. Comb. 31(2):P2.31, 2024). Here, we investigate the existence of cubic $\ell$-circulant nut graphs for $\ell \geq 4$ and show that there is no cubic $4$-circulant nut graph or cubic $5$-circulant nut graph by using a computer-assisted proof. Furthermore, we rely on a construction based approach in order to demonstrate that there exist infinitely many cubic $\ell$-circulant nut graphs for any fixed $\ell \in \{6, 7\}$ or $\ell \geq 9$. |
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| Keywords: | nut graph, polycirculant graph, cubic graph, pregraph, voltage graph |
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| Publication date: | 06.05.2025 |
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| Year of publishing: | 2025 |
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| Number of pages: | str. 1-18 |
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| Numbering: | Vol. 44, iss. 5, article no. 265 |
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| PID: | 20.500.12556/RUP-22123  |
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| UDC: | 519.17 |
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| ISSN on article: | 2238-3603 |
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| DOI: | 10.1007/s40314-025-03218-7 |
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| COBISS.SI-ID: | 257859075 |
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| Publication date in RUP: | 19.11.2025 |
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| Views: | 271 |
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| Downloads: | 5 |
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