20.500.12556/RUP-22123 On cubic polycirculant nut graphs 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 $\ell \geq 9$. nut graph polycirculant graph cubic graph pregraph voltage graph orešni graf policirkulantni graf kubični graf predgraf napetostni graf true false true Angleški jezik Slovenski jezik Članek v reviji 2025-11-19 15:21:20 2025-11-19 15:21:23 2025-11-22 03:03:53 0000-00-00 00:00:00 2025 0 0 str. 1-18 iss. 5, article no. 265 Vol. 44 Jul. 2025 0000-00-00 NiDoloceno NiDoloceno NiDoloceno 0000-00-00 0000-00-00 2025-05-06 519.17 2238-3603 10.1007/s40314-025-03218-7 257859075 RAZ_Basic_Nino_2025.pdf RAZ_Basic_Nino_2025.pdf 1 BF277F4DDD8652434F814319A5E120B7 42fbad40bfad79bb602b9c9e01450c5de8ebc3a6adef296c41c04d8c4a9afe8b 98f2db1a-c553-11f0-8f0b-005056ac49c0 https://repozitorij.upr.si/Dokument.php?lang=slv&id=32085 https://link.springer.com/article/10.1007/s40314-025-03218-7 1 456cb264-c553-11f0-8f0b-005056ac49c0 https://repozitorij.upr.si/Dokument.php?lang=slv&id=32084 Fakulteta za matematiko, naravoslovje in informacijske tehnologije 0 0 0