Regularity of edge ideals of powers of graphs

TL;DR

This paper investigates the algebraic property called regularity of edge ideals derived from graph powers, showing it decreases for forests and providing exact values for cycles, advancing understanding in combinatorial commutative algebra.

Contribution

It proves the regularity of edge ideals of powers of forests is weakly decreasing and computes the regularity for powers of cycles, offering new insights into graph algebra.

Findings

Regularity of edge ideals of forests' powers is weakly decreasing.

Exact regularity values are computed for powers of cycles.

Provides new algebraic characterizations for specific graph classes.

Abstract

We prove that the regularity of edge ideals of powers of forests is weakly decreasing. We then compute the regularity of edge ideals of powers of cycles.