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In this paper, we discuss the normality of the toric rings of stable setpolytopes, and the set of generators and Gr\"obner bases of toric ideals ofstable set polytopes by using the results on that of edge polytopes of finitenonsimple graphs. In particular, for a graph of stability number two, we give agraph theoretical characterization of the set of generators of the toric idealof the stable set polytope, and a criterion to check whether the toric ring ofthe stable set polytope is normal or not. One of the application of the resultsis an infinite family of stable set polytopes whose toric ideal is generated byquadratic binomials and has no quadratic Gr\"obner bases.

Toric rings and ideals of stable set polytopes