Depth of Binomial Edge Ideals in terms of Diameter and Vertex Connectivity
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arXiv
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| Format: | Preprint |
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2021
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| _version_ | 1866909153183662080 |
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| author | Jayanthan, A. V. Sarkar, Rajib |
| author_facet | Jayanthan, A. V. Sarkar, Rajib |
| contents | 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 Núñez-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 $G$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2112_04835 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Depth of Binomial Edge Ideals in terms of Diameter and Vertex Connectivity Jayanthan, A. V. Sarkar, Rajib Commutative Algebra Combinatorics 13D02, 13C13, 05E40 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 Núñez-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 $G$. |
| title | Depth of Binomial Edge Ideals in terms of Diameter and Vertex Connectivity |
| topic | Commutative Algebra Combinatorics 13D02, 13C13, 05E40 |
| url | https://arxiv.org/abs/2112.04835 |