Regularity of normal Rees algebras of edge ideals of graphs

TL;DR

This paper classifies graphs whose edge ideal Rees algebras are normal and have regularity equal to their matching number, linking algebraic properties with combinatorial graph invariants.

Contribution

It provides a complete classification of graphs with normal Rees algebras of edge ideals having regularity equal to their matching number.

Findings

Identifies all graphs with normal Rees algebras and specific regularity properties.

Establishes a connection between algebraic regularity and graph matching number.

Offers a comprehensive classification in this algebraic-combinatorial context.

Abstract

We classify all graphs for which the Rees algebras of their edge ideals are normal and have regularity equal to their matching numbers.