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 $3 \leq d \leq 12$ and for $d \geq 4$ such that $d \equiv 0 \pmod{4}$. Here it is shown that infinitely many $d$-regular nut graphs exist for each degree $d \geq 3$. Likewise, it is known that infinitely many $d$-regular Cayley nut graphs exist for $d \geq 4$ such that $d \equiv 0 \pmod{4}$. Here we prove that there are infinitely many $d$-regular Cayley nut graphs for each even $d \ge 4$. This implies that we have identified all feasible degrees $d$ for which a $d$-regular Cayley nut graph exists.

Rights

URN

URN:NBN:SI:DOC-C6965GLZ

COBISSID

264594691

DOI

10.26493/1855-3974.3641.49c

Added

27.10.2026

Metadata

Citation

APA:

Bašić, Nino, Damnjanović, Ivan, Fowler, Patrick W. (2026). On the degrees of regular nut graphs and Cayley nut graphs. Ars mathematica contemporanea, , article, str. 1-15. URN:NBN:SI:DOC-C6965GLZ from http://www.dlib.si

MLA:

Bašić, Nino, Damnjanović, Ivan, Fowler, Patrick W.. "On the degrees of regular nut graphs and Cayley nut graphs." Ars mathematica contemporanea . article (2026) str. 1-15.
<http://www.dlib.si/?URN=URN:NBN:SI:DOC-C6965GLZ>

Ars mathematica contemporanea
2008-
(Assembly record)