The Jacobian of a graph and graph automorphisms

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F49777513%3A23520%2F25%3A43972823" target="_blank" >RIV/49777513:23520/25:43972823 - isvavai.cz</a>
Result on the web
<a href="https://www.sciencedirect.com/science/article/pii/S0012365X2400390X?pes=vor" target="_blank" >https://www.sciencedirect.com/science/article/pii/S0012365X2400390X?pes=vor</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.disc.2024.114259" target="_blank" >10.1016/j.disc.2024.114259</a>

Result language
angličtina
Original language name
The Jacobian of a graph and graph automorphisms
Original language description
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.
Czech name
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Czech description
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Type
J<sub>SC</sub> - Article in a specialist periodical, which is included in the SCOPUS database
CEP classification
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OECD FORD branch
10101 - Pure mathematics

Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2025
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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