2021/02/08 by Bašić, Nino, Knor, Martin, Škrekovski, Riste · 2 citations
#05C50 #15A18 #Combinatorics (math.CO) #FOS: Mathematics
paper · doi:10.48550/arxiv.2102.04418
A nut graph is a simple graph whose adjacency matrix is singular with 1-dimensional kernel such that the corresponding eigenvector has no zero entries. In 2020, Fowler et al. characterised for each d ∈ \3,4,…,11\ all values n such that there exists a d-regular nut graph of order n. In the present paper, we determine all values n for which a 12-regular nut graph of order n exists. We also present a result by which there are infinitely many circulant nut graphs of degree d ≡ 0 \pmod 4 and no circulant nut graph of degree d ≡ 2 \pmod 4.