Cochordal zero divisor graphs and Betti numbers of their edge ideals

We associate a sequence of positive integers, termed the type sequence, with a cochordal graph. Using this type sequence, we compute all graded Betti numbers of its edge ideal. We then classify all positive integer \(n\) such that the zero divisor graph of \(\mathbb{Z}/n \mathbb{Z}\) is cochordal and determine all the graded Betti numbers of its edge ideal.