Geodesic
On cyclic vertices in valued translation quivers
Piotr Malicki 1
1 Faculty of Mathematics and Computer Science Nicolaus Copernicus University Chopina 12/18 87-100 Toruń, Poland
Colloquium Mathematicum, Tome 105 (2006) no. 1, pp. 45-50 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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Let $x$ and $y$ be two vertices lying on an oriented cycle in a connected valued translation quiver $(\Gamma , \tau , \delta )$. We prove that, under certain conditions, $x$ and $y$ belong to the same cyclic component of $(\Gamma , \tau , \delta )$ if and only if there is an oriented cycle in $(\Gamma , \tau , \delta )$ passing through $x$ and $y$.
DOI : 10.4064/cm105-1-5
Keywords: vertices lying oriented cycle connected valued translation quiver gamma tau delta prove under certain conditions belong cyclic component gamma tau delta only there oriented cycle gamma tau delta passing through

Piotr Malicki  1

1 Faculty of Mathematics and Computer Science Nicolaus Copernicus University Chopina 12/18 87-100 Toruń, Poland 
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Piotr Malicki. On cyclic vertices in valued translation quivers. Colloquium Mathematicum, Tome 105 (2006) no. 1, pp. 45-50. doi: 10.4064/cm105-1-5

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