  In this note we study the eigenvalue growth of infinite graphs with discrete
spectrum. We assume that the corresponding Dirichlet forms satisfy certain
Sobolev-type inequalities and that the total measure is finite. In this sense,
the associated operators on these graphs display similarities to elliptic
operators on bounded domains in the continuum. Specifically, we prove lower
bounds on the eigenvalue growth and show by examples that corresponding upper
bounds can not be established.
