Research article

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

  • 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.

    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

    Related Papers:

  • 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.



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