Approximations of permutation-symmetric vertex couplings in quantum graphs

Abstract

We consider boundary conditions at the vertex of a star graph which make Schroedinger operators on the graph self-adjoint, in particular, the two-parameter family of such conditions invariant with respect to permutations of graph edges. It is proved that the corresponding operators can be approximated in the norm-resolvent sense by elements of another Schroedinger operator family on the same graph in which the delta coupling is imposed at the vertex and an additional point interaction is placed at each edge provided the coupling parameters are properly chosen.