On Jacobian group and complexity of the $Y$-graph

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.