We consider the Schrodinger operators on graphs with a finite or
countable number of edges and Schr?dinger operators on branched manifolds of
variable dimension. In particular, a description of self-adjoint extensions of
symmetric Schr?dinger operator, initially defined on a smooth function, whose
support does not contain the branch points of the graph and branch points of
the manifold. These results are
obtained for graphs with a single vertex, graphs with multiple vertices and
graphs with a single vertex and countable set of rays.
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