Ehrhart series of fractional stable set polytopes of finite graphs

The fractional stable set polytope $\mathrm{F}\mathrm{R}\mathrm{A}\mathrm{C}(G)$ of a simple graph $G$ with $d$ vertices is a rational polytope that is the set of nonnegative vectors $(x_1,\dots ,x_d)$ satisfying $x_i+x_j\le 1$ for every edge $(i,j)$ of $G$. In this paper we show that (i) The $\delta$-vector of a lattice polytope $2 {\rm FRAC}(G)$isalternatinglyincreasing;(ii)TheEhrhartringof${\rm FRAC}(G)$isGorenstein;(iii)ThecoefficientsofthenumeratoroftheEhrhartseriesof${\rm FRAC}(G)$aresymmetric,unimodalandcomputedbythe$\delta$-vectorof$2 {\rm FRAC}(G)$.