  The space C of conservative vertex colorings (over a field F) of a countable,
locally finite graph G is introduced. The subspace of based colorings is shown
to be isomorphic to the bicycle space of the graph. For graphs G with a free
Z^d-action by automorphisms, C is a finitely generated module over the
polynomial ring F[Z^d], and for this a polynomial invariant, the Laplacian
polynomial, is defined. Properties of this polynomial are discussed. The
logarithmic Mahler measure of the Laplacian polynomial is characterized in
terms of the growth of spanning trees of G.
