The fractional stable set polytope FRAC(G) of a simple graph G with d vertices is a rational polytope that is the set of nonnegative vectors (x1, . . . , xd) satisfying xi + xj(Formula presented.) 1 for every edge (i, j) of G. In this paper we show that (i) the (Formula presented.)-vector of a lattice polytope 2FRAC(G) is alternatingly increasing, (ii) the Ehrhart ring of FRAC(G) is Gorenstein, (iii) the coefficients of the numerator of the Ehrhart series of FRAC(G) are symmetric, unimodal and computed by the (Formula presented.)-vector of 2FRAC(G).