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

Malik Muhammad Suleman Shahid; Muhammad Ishaq; Anuwat Jirawattanapanit; Khanyaluck Subkrajang; Malik Muhammad Suleman Shahid; Muhammad Ishaq; Anuwat Jirawattanapanit; Khanyaluck Subkrajang

doi:10.3934/math.2022900

AIMS Mathematics

2022, Volume 7, Issue 9: 16449-16463. doi: 10.3934/math.2022900

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Research article

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

1.
School of Natural Sciences, National University of Sciences and Technology Islamabad, Sector H-12, Islamabad, Pakistan
2.
Department of Mathematics, Faculty of Science, Phuket Rajabhat University (PKRU), 6 Thepkasattree Road, Raddasa, Phuket 83000, Thailand
3.
Faculty of Science and Technology, Rajamangala University of Technology Suvarnabhumi, 7/1 Village No. 1, Nonthaburi 1 Road, Suan Yai Sub-district, Muang District, Nonthaburi 11000, Thailand

Received: 01 April 2022 Revised: 20 June 2022 Accepted: 28 June 2022 Published: 07 July 2022
MSC : Primary: 13C15; Secondary: 13P10, 13F20

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.
- depth,
- Stanley depth,
- monomial ideal,
- edge ideal,
- triangular snake graph,
- multi triangular snake graph,
- triangular ouroboros snake graph,
- multi triangular ouroboros snake graph
Citation: Malik Muhammad Suleman Shahid, Muhammad Ishaq, Anuwat Jirawattanapanit, Khanyaluck Subkrajang. Depth and Stanley depth of the edge ideals of multi triangular snake and multi triangular ouroboros snake graphs[J]. AIMS Mathematics, 2022, 7(9): 16449-16463. doi: 10.3934/math.2022900

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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.

References

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