Winter 2024 DEPTH OF BINOMIAL EDGE IDEALS IN TERMS OF DIAMETER AND VERTEX CONNECTIVITY
A. V. Jayanthan, Rajib Sarkar
J. Commut. Algebra 16(4): 411-437 (Winter 2024). DOI: 10.1216/jca.2024.16.411

Abstract

Let G be a simple connected noncomplete graph and JG be its binomial edge ideal in a polynomial ring S. Using certain invariants associated to graphs, say U(G), Banerjee and Núñez-Betancourt gave an upper bound for the depth of SJG, and Rouzbahani Malayeri, Saeedi Madani and Kiani obtained a lower bound, say L(G). Hibi and Saeedi Madani gave a structural classification of graphs satisfying L(G)=U(G). In this article, we give structural classification of graphs satisfying L(G)+1=U(G). We also compute the depth of SJG for all such graphs G.

Citation

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A. V. Jayanthan. Rajib Sarkar. "DEPTH OF BINOMIAL EDGE IDEALS IN TERMS OF DIAMETER AND VERTEX CONNECTIVITY." J. Commut. Algebra 16 (4) 411 - 437, Winter 2024. https://doi.org/10.1216/jca.2024.16.411

Information

Received: 9 August 2022; Revised: 4 January 2024; Accepted: 7 March 2024; Published: Winter 2024
First available in Project Euclid: 6 January 2025

MathSciNet: MR3566527
Digital Object Identifier: 10.1216/jca.2024.16.411

Subjects:
Primary: 05E40 , 13C13 , 13D02

Keywords: binomial edge ideal , depth , diameter , vertex connectivity

Rights: Copyright © 2024 Rocky Mountain Mathematics Consortium

Vol.16 • No. 4 • Winter 2024
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