A Characterization of Triangle-free Gorenstein graphs and Cohen-Macaulayness of second powers of edge ideals

TL;DR

This paper characterizes triangle-free Gorenstein graphs using graph theory and determines conditions under which the square of their edge ideals is Cohen-Macaulay, linking graph properties with algebraic properties.

Contribution

It provides a graph-theoretic characterization of triangle-free Gorenstein graphs and classifies when the second power of their edge ideals is Cohen-Macaulay.

Findings

Characterization of triangle-free Gorenstein graphs

Classification of Cohen-Macaulayness of $I(G)^2$

Connection between graph properties and algebraic conditions

Abstract

We graph-theoretically characterize triangle-free Gorenstein graphs $G$. As an application, we classify when $I(G)^2$ is Cohen-Macaulay.