Schrodinger operators with locally integrable potentials on infinite metric graphs

The paper is devoted to Schrodinger operators on infinite metric graphs. We suppose that the potential is locally integrable and its negative part is bounded in certain integral sense. First, we obtain a description of the bottom of the essential spectrum. Then we prove theorems on the discreteness of the negative part of the spectrum and of the whole spectrum that extend some classical results for one dimensional Schrodinger operators.