English

Abstract

Let o(n) be the greatest odd integer less than or equal to n. In this paper we provide explicit formulae to compute ℕ-graded Betti numbers of the circulant graphs C2n(1, 2, 3, 5, …, o(n)). We do this by showing that this graph is the product (or join) of the cycle Cn by itself, and computing Betti numbers of Cn * Cn. We also discuss whether such a graph (more generally, G * H) is well-covered, Cohen-Macaulay, sequentially Cohen-Macaulay, Buchsbaum, or S2.