Nut graphs with a prescribed number of vertex and edge orbits
Abstract
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.
Fields of Study & Subjects
Graph theory and applications
Finite Group Theory Research
Interconnection Networks and Systems
Publication details
- Journal / source
- Journal of Algebraic Combinatorics
- Publisher
- Springer Science and Business Media LLC
- Volume
- 63
- Issue
- 1
- Publication date
- 8 January 2026
- Language
- EN