Graded Betti numbers of some circulant graphs

Abstract

Let G be the circulant graph C n (S) with S ⊆ {1, 2, . . . , n 2 }, and let I(G) denote the edge ideal in the polynomial ring R = K[x 0 , x 1 , . . . , x n−1 ] over a field K. In this paper, we compute the N-graded Betti numbers of the edge ideals of three families of circulant graphs C n (1, 2, . . . ,