For \(l\)-regular graphs associated to regular tesselations of the hyperbolic plane by \(m\)-gons, the denominators of the growth series are shown to be essentially irreducible reciprocal Salem polynomials. Consequently the growth rates of these graphs are Salem numbers. These results extend results of J. W. Cannon and P. Wagreich [Math. Ann. 293, No. 2, 239–258 (1992; Zbl 0734.57001)]. Moreover, some regularity properties of the coefficients for the growth series are derived.