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

AIMS Mathematics

article

Malik Muhammad Suleman Shahid¹  Muhammad Ishaq¹  Anuwat Jirawattanapanit²  Khanyaluck Subkrajang³ 

[1] School of Natural Sciences, National University of Sciences and Technology Islamabad;Department of Mathematics, Faculty of Science, Phuket Rajabhat University;Faculty of Science and Technology, Rajamangala University of Technology Suvarnabhumi

关键词: depth;    Stanley depth;    monomial ideal;    edge ideal;    triangular snake graph;    multi triangular snake graph;    triangular ouroboros snake graph;    multi triangular ouroboros snake graph;   

DOI  :  10.3934/math.2022900

学科分类：地球科学(综合)

来源: AIMS Press

【 摘 要 】

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.

【 授权许可】

CC BY