On a representation of the automorphism group of a graph in a unimodular group

Kód výsledku v IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F49777513%3A23520%2F21%3A43962836" target="_blank" >RIV/49777513:23520/21:43962836 - isvavai.cz</a>
Výsledek na webu
<a href="https://www.sciencedirect.com/science/article/pii/S0012365X21003198" target="_blank" >https://www.sciencedirect.com/science/article/pii/S0012365X21003198</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.disc.2021.112606" target="_blank" >10.1016/j.disc.2021.112606</a>

Jazyk výsledku
angličtina
Název v původním jazyce
On a representation of the automorphism group of a graph in a unimodular group
Popis výsledku v původním jazyce
We investigate a representation of the automorphism group of a connected graph X in the group of unimodular matrices U(b) of dimension b, where b is the Betti number of graph X. We classify the graphs for which the automorphism group does not embed into U(b) . It follows that if X has no pendant vertices and X is not a simple cycle, then the representation is faithful and Aut(X) acts faithfully on homology group H(X, Z). The latter statement can be viewed as a discrete analogue of a classical Hurwitz’s theorem on Riemann surfaces of genera greater than one.
Název v anglickém jazyce
On a representation of the automorphism group of a graph in a unimodular group
Popis výsledku anglicky
We investigate a representation of the automorphism group of a connected graph X in the group of unimodular matrices U(b) of dimension b, where b is the Betti number of graph X. We classify the graphs for which the automorphism group does not embed into U(b) . It follows that if X has no pendant vertices and X is not a simple cycle, then the representation is faithful and Aut(X) acts faithfully on homology group H(X, Z). The latter statement can be viewed as a discrete analogue of a classical Hurwitz’s theorem on Riemann surfaces of genera greater than one.

Projekt
<a href="/cs/project/GA20-15576S" target="_blank" >GA20-15576S: Nakrývání grafů: Symetrie a složitost</a><br>
Návaznosti
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění
2021
Kód důvěrnosti údajů
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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