Year: 2026
Type: article
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 $$r \ge 2$$ r ≥ 2 and any $$k \ge r + 1$$ k ≥ 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 $$k \ge 2$$ k ≥ 2 , there are infinitely many Cayley nut graphs with k edge orbits and k arc orbits.
Authors: Nino Bašić, Ivan Damnjanović
Language: English
Topic: Finite Group Theory Research
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,090
OpenAlex ID: W4416150644