# Regularity of the edge ideals of perfect [ν,h]-ary trees and some unicyclic graphs

## TL;DR

This paper calculates a specific algebraic property called regularity for certain types of tree and unicyclic graph structures.

## Contribution

The paper introduces new computations of Castelnuovo-Mumford regularity for edge ideals of specific tree and unicyclic graphs.

## Key findings

- The Castelnuovo-Mumford regularity of quotient rings for perfect [ν,h]-ary trees is computed.
- Regularity is also determined for some unicyclic graphs.

## Abstract

We compute the Castelnuovo-Mumford regularity of the quotient rings of edge ideals of perfect [ν,h]-ary trees and some unicyclic graphs.