  We consider operators arising from regular Dirichlet forms with vanishing
killing term. We give bounds for the bottom of the (essential) spectrum in
terms of exponential volume growth with respect to an intrinsic metric. As
special cases we discuss operators on graphs. When the volume growth is
measured in the natural graph distance (which is not an intrinsic metric) we
discuss the threshold for positivity of the bottom of the spectrum and
finiteness of the bottom of the essential spectrum of the (unbounded) graph
Laplacian. This threshold is shown to lie at cubic polynomial growth.
