Nut graphs with a given automorphism group

Fuente: arXiv
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Main Authors: Bašić, Nino, Fowler, Patrick W.
Format: Preprint
Published: 2024
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author Bašić, Nino
Fowler, Patrick W.
author_facet Bašić, Nino
Fowler, Patrick W.
contents 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 non-zero 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.
format Preprint
id arxiv_https___arxiv_org_abs_2405_04117
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Nut graphs with a given automorphism group
Bašić, Nino
Fowler, Patrick W.
Combinatorics
05C25, 05C50
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 non-zero 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.
title Nut graphs with a given automorphism group
topic Combinatorics
05C25, 05C50
url https://arxiv.org/abs/2405.04117