On the Stanley depth and Hilbert depth of some classes of edge ideals of graphs

TL;DR

This paper investigates the Stanley depth and Hilbert depth of edge ideals associated with various classes of graphs, including paths, cycles, stars, and double brooms, to understand their algebraic properties.

Contribution

It provides new insights into the depths of edge ideals for specific graph classes, expanding the understanding of their algebraic invariants.

Findings

Determined the Stanley depth for edge ideals of path and cycle graphs.

Calculated the Hilbert depth for generalized star and double broom graphs.

Established bounds and exact values for depths in several graph classes.

Abstract

We study the Stanley depth and the Hilbert depth of the edge ideals of path graphs, cycle graphs, generalized star graphs and double broom graphs.