circulant s2 graphs

In 2016, earl, vander meulen, and van tuyl characterized some families of cohen-macaulay or buchsbaum circulant graphs discovered by boros-gurvich-milanič, brown-hoshino, and moussi. in this paper, we will characterize those families of circulant graphs which satisfy serre’s condition s2. more precisely, we show that for some families of circulant graphs, s2 property is equivalent to well-coveredness or buchsbaumness, and for some other families, it is equivalent to cohen-macaulayness. we also give some examples of infinite families of circulant graphs which are buchsbaum but not s2, and vice versa.