A Sears-type self-adjointness result for discrete magnetic Schrodinger 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 Delta(sigma) + W, where Delta(sigma) is the magnetic Laplacian and W: V -> R is a function satisfying W(x) >= -q(x) for all X is an element of V, with q: V -> [ 1, infinity). 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. (C) 2012 Elsevier Inc. All rights reserved.