On the degrees of regular nut graphs and Cayley nut graphs
Abstract
A nut graph is a simple graph for which the adjacency matrix has a single zero eigenvalue such that all non-zero kernel eigenvectors have no zero entry. It is known that infinitely many d-regular nut graphs exist for 3 ≤ d ≤ 12 and for d ≥ 4 such that d ≡ 0 (mod 4). Here it is shown that infinitely many d-regular nut graphs exist for each degree d ≥ 3. Moreover, we prove that there are infinitely many d-regular Cayley nut graphs for each even d ≥ 4. This implies that we have identified all feasible degrees d for which a d-regular Cayley nut graph exists.
Fields of Study & Subjects
Graph theory and applications
Finite Group Theory Research
Advanced Graph Theory Research
Publication details
- Journal / source
- Ars Mathematica Contemporanea
- Volume
- 26
- Issue
- 4
- Pages
- #P4.10–#P4.10
- Publication date
- 13 January 2026
- Language
- EN