The Jacobian of a graph and graph automorphisms Full article
| Journal |
Discrete Mathematics
ISSN: 0012-365X , E-ISSN: 1872-681X |
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| Output data | Year: 2025, Volume: 348, Number: 2, Article number : 114259, Pages count : 8 DOI: 10.1016/j.disc.2024.114259 | ||||||||||
| Tags | Graph, Flow, Automorphism, Jacobian | ||||||||||
| Authors |
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| Affiliations |
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Funding (1)
| 1 | Sobolev Institute of Mathematics | FWNF-2022-0005 |
Abstract:
In the present paper we investigate the faithfulness of certain linear representations of groups of automorphisms of a graph X in the group of symmetries of the Jacobian of X. As a consequence we show that if a 3-edge-connected graph X admits a nonabelian semiregular group of automorphisms, then the Jacobian of X cannot be cyclic. In particular, Cayley graphs of degree at least three arising from nonabelian groups have non-cyclic Jacobians. While the size of the Jacobian of X is well-understood – it is equal to the number of spanning trees of X– the combinatorial interpretation of the rank of Jacobian of a graph is unknown. Our paper presents a contribution in this direction.
Cite:
Estélyi I.
, Karabáš J.
, Mednykh A.
, Nedela R.
The Jacobian of a graph and graph automorphisms
Discrete Mathematics. 2025. V.348. N2. 114259 :1-8. DOI: 10.1016/j.disc.2024.114259 WOS Scopus РИНЦ OpenAlex
The Jacobian of a graph and graph automorphisms
Discrete Mathematics. 2025. V.348. N2. 114259 :1-8. DOI: 10.1016/j.disc.2024.114259 WOS Scopus РИНЦ OpenAlex
Dates:
| Submitted: | Dec 22, 2022 |
| Accepted: | Sep 4, 2024 |
| Published online: | Sep 11, 2024 |
| Published print: | Feb 5, 2025 |
Identifiers:
| Web of science: | WOS:001315207200001 |
| Scopus: | 2-s2.0-85203432938 |
| Elibrary: | 80690076 |
| OpenAlex: | W4402448510 |
Citing:
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