A Sears-type self-adjointness result for discrete magnetic Schrödinger operators

In the context of a weighted graph with vertex set V and bounded vertex degree, we give a sufficient condition for the essential self-adjointness of the operator Δσ+W, where Δσ is the magnetic Laplacian and W:V→R is a function satisfying W(x)≥−q(x) for all x∈V, with q:V→[1,∞). The condition is expressed in terms of completeness of a metric that depends on q and the weights of the graph. The main result is a discrete analogue of the results of I. Oleinik and M.A. Shubin in the setting of non-compact Riemannian manifolds.