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We discuss approximations of vertex couplings of quantum graphs usingfamilies of thin branched manifolds. We show that if a Neumann type Laplacianon such manifolds is amended by suitable potentials, the resultingSchr\"odinger operators can approximate non-trivial vertex couplings. Thelatter include not only the delta-couplings but also those with wavefunctionsdiscontinuous at the vertex. We work out the example of the symmetricdelta'-couplings and conjecture that the same method can be applied to allcouplings invariant with respect to the time reversal.

Approximation of quantum graph vertex couplings by scaled Schr\"odinger operators on thin branched manifolds