# The regularity of some families of circulant graphs

## TL;DR

This paper calculates the Castelnuovo-Mumford regularity of edge ideals for specific families of circulant graphs, including all cubic ones, using bounds on algebraic invariants to find exact values.

## Contribution

It introduces a method combining bounds on regularity, projective dimension, and Euler characteristic to precisely determine the regularity of these graph families.

## Key findings

- Exact regularity values for the studied circulant graphs
- Method applicable to a broad class including cubic circulant graphs
- Enhanced understanding of algebraic properties of circulant graphs

## Abstract

We compute the Castelnuovo-Mumford regularity of the edge ideals of two families of circulant graphs, which includes all cubic circulant graphs. A feature of our approach is to combine bounds on the regularity, the projective dimension, and the reduced Euler characteristic to derive an exact value for the regularity.