20.500.12556/RUP-22449 Nut graphs with a prescribed number of vertex and edge orbits 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. nut graph vertex orbit edge orbit arc orbit Cayley graph automorphism orešni graf orbita vozlišč orbita povezav orbita lokov Cayleyjev graf avtomorfizem true false true Angleški jezik Slovenski jezik Članek v reviji 2026-01-09 15:22:20 2026-01-09 15:22:21 2026-01-13 03:05:32 0000-00-00 00:00:00 2026 0 0 str. 1-12 iss. 1, article no. 9 Vol. 63 Jan. 2026 0000-00-00 Zaloznikova NiDoloceno NiDoloceno 0000-00-00 0000-00-00 2026-01-08 519.17 0925-9899 264172035 RAZ_Basic_Nino_2026.pdf RAZ_Basic_Nino_2026.pdf 1 88A373D5D6B2922A8B9EE3E1E3221868 7899debd8bc2555e220026fb0bcb2234e3a632da68a31eeb3df23451319886d1 b77acbb8-ed66-11f0-8639-005056ac49c0 https://repozitorij.upr.si/Dokument.php?lang=slv&id=32639 https://link.springer.com/article/10.1007/s10801-025-01492-6 1 9dbb5c21-ed66-11f0-8639-005056ac49c0 https://repozitorij.upr.si/Dokument.php?lang=slv&id=32638 Fakulteta za matematiko, naravoslovje in informacijske tehnologije 0 0 0