Year: 2025
Type: article
Abstract: A nut graph is a simple graph of order 2 or more for which the adjacency matrix has a single zero eigenvalue such that all nonzero kernel eigenvectors have no zero entry (i.e. are full). It is shown by construction that every finite group can be represented as the group of automorphisms of infinitely many nut graphs. It is further shown that such nut graphs exist even within the class of regular graphs; the cases where the degree is 8, 12, 16, 20 or 24 are realised explicitly.
Authors: Nino Bašić, Patrick W. Fowler
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,090
Awards: Computationally intensive methods in theoretical computer science, discrete mathematics, combinatorial optimization, and numerical analysis and algebra with applications in natural and social sciences, Geometries, Graphs, Groups and their Links, Mathematical and computational methods for polyhedral self-assembly
OpenAlex ID: W4407716422