71. Nut graphs with a prescribed number of vertex and edge orbitsNino Bašić, Ivan Damnjanović, 2026, izvirni znanstveni članek Opis: 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.
Ključne besede: nut graph, vertex orbit, edge orbit, arc orbit, Cayley graph, automorphism
Objavljeno v RUP: 09.01.2026; Ogledov: 188; Prenosov: 5
 Celotno besedilo (445,35 KB)
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