Depth and Stanley depth of the edge ideals of multi triangular snake and multi triangular ouroboros snake graphs

Abstract

In this paper, we study depth and Stanley depth of the quotient rings of the edge ideals associated to triangular and multi triangular snake and triangular and multi triangular ouroboros snake graphs. In some cases, we find exact values, otherwise, we find tight bounds. We also find lower bounds for the edge ideals of triangular and multi triangular snake and ouroboros snake graphs and prove a conjecture of Herzog for all edge ideals we considered.

Keywords

• depth
• stanley depth
• monomial ideal
• edge ideal
• triangular snake graph
• multi triangular snake graph
• triangular ouroboros snake graph
• multi triangular ouroboros snake graph