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 $\mathbb{Z}\mathrm{/}n\mathbb{Z}$ is cochordal and determine all the graded Betti numbers of its edge ideal.