In this paper we consider the Schrödinger operator on the noncompact starshaped metric graph with short-range perturbation of the potential of the form __ іп the neighborhood of the vertex. We study the asymptotic behavior, as  __ of spectrum and eigenfunctions of such a Hamiltonian. We obtain the limit operator which is a generahzation of the Schrödrnger operator with the ___ -potential on a line.

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