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Research Article | Open Access

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

Malik Muhammad Suleman Shahid1, Muhammad Ishaq1, Anuwat Jirawattanapanit2, Khanyaluck Subkrajang3( )
School of Natural Sciences, National University of Sciences and Technology Islamabad, Sector H-12, Islamabad, Pakistan
Department of Mathematics, Faculty of Science, Phuket Rajabhat University (PKRU), 6 Thepkasattree Road, Raddasa, Phuket 83000, Thailand
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
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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.

Keywords

depthStanley depthmonomial idealedge idealtriangular snake graphmulti triangular snake graphtriangular ouroboros snake graphmulti triangular ouroboros snake graph
CLC number: Primary: 13C15; Secondary: 13P10, 13F20

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AIMS Mathematics
Volume 7 Issue 9,
September 2022
Pages 16449-16463
DOI: 10.3934/math.2022900

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Cite this article:
Shahid MMS, Ishaq M, Jirawattanapanit A, et al. Depth and Stanley depth of the edge ideals of multi triangular snake and multi triangular ouroboros snake graphs. AIMS Mathematics, 2022, 7(9): 16449-16463. https://doi.org/10.3934/math.2022900

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Received: 01 April 2022
Revised: 20 June 2022
Accepted: 28 June 2022
Published: 15 September 2022
©2022 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)