Cohen–Macaulayness of two classes of circulant graphs

Abstract

Let n be a positive integer and let $$S_n$$ be the set of all nonnegative integers less than n which are relatively prime to n. In this paper, we discuss structural properties of circulant graphs generated by the $$S_n$$ ’s and their complements. In particular, we characterize when these graphs are well-covered, Cohen–Macaulay, Buchsbaum or Gorenstein.