Cochordal zero divisor graphs and Betti numbers of their edge ideals

Abstract

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 Z/n Z is cochordal and determine all the graded Betti numbers of its edge ideal.

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