Magnetic-Sparseness and Schrödinger Operators on Graphs

Abstract

Abstract We study magnetic Schrödinger operators on graphs. We extend the notion of sparseness of graphs by including a magnetic quantity called the frustration index. This notion of magnetic-sparseness turns out to be equivalent to the fact that the form domain is an $$\ell ^{2}$$ℓ2 space. As a consequence, we get criteria of discreteness for the spectrum and eigenvalue asymptotics.