We give a sufficient condition for the essential self-adjointness of a
perturbation of the square of the magnetic Laplacian on an infinite weighted
graph. The main result is applicable to graphs whose degree function is not
necessarily bounded. The result allows perturbations that are not necessarily
bounded from below by a constant.Comment: We edited the introduction and updated the bibliographical
information for some references. We moved the examples towards the front of
the articl
