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arXiv · 2112.04835

Depth of Binomial Edge Ideals in terms of Diameter and Vertex Connectivity

A. V. Jayanthan·Rajib Sarkar
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Abstract

Let $G$ be a simple connected non-complete graph and $J_G$ be its binomial edge ideal in a polynomial ring $S$. Using certain invariants associated to graphs, say $U(G)$, Banerjee and N\'{u}\~{n}ez-Betancourt gave an upper bound for the depth of $S/J_G$, 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 $S/J_G$ for all such graphs $G$.

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A. V. Jayanthan, Rajib Sarkar. 2021-12-09. Depth of Binomial Edge Ideals in terms of Diameter and Vertex Connectivity. https://arxiv.org/abs/2112.04835

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