Geodesic
On Jacobian group and complexity of the $Y$-graph
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 19 (2022) no. 2, pp. 662-673

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In the present paper we suggest a simple approach for counting Jacobian group of the $Y$-graph $Y(n; k, l, m).$ In the case $Y(n; 1, 1, 1)$ the structure of the Jacobian group will be find explicitly. Also, we obtain a closed formula for the number of spanning trees of $Y$-graph in terms of Chebyshev polynomials and give its asymtotics.
Keywords: spanning tree, Chebyshev polynomial, Mahler measure.
Mots-clés : Jacobian group, Laplacian matrix 
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     title = {On {Jacobian} group and complexity of the $Y$-graph},
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Y. S. Kwon; A. D. Mednykh; I. A. Mednykh. On Jacobian group and complexity of the $Y$-graph. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 19 (2022) no. 2, pp. 662-673. http://geodesic.mathdoc.fr/item/SEMR_2022_19_2_a51/