Abstract
The spectrum discreteness Molchanov's condition for a potential on the real axis (or half-axis) is well known. The goal of this work is to obtain an analogous condition for a quantum graph. We deal with δ-type conditions at the graph vertices. The Schrodinger operator with a potential is considered at each edge. It is assumed that the graph has infinite leads (edges) or/and infinite chains of vertices such that the neighbouring vertices are connected by finite number of edges. Molchanov-type theorem for the quantum graph Hamiltonian spectrum discreteness is proved.
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