The electronic properties of the wormhole and the perturbed nanocylinder were investigated using two different methods: the continuum gauge field-theory model that deals with the continuum approximation of the surface and the Haydock recursion method that transforms the surface into a simplier structure and deals with the nearest-neighbor interactions. Furthermore, the changes of the electronic properties were investigated for the case of enclosing the appropriate structure, and possible substitutes for the encloser were derived. Finally, the character of the electron flux through the perturbed wormhole was predicted from the model based on the multiwalled nanotubes. The effect of the "graphene blackhole" is introduced.