用直径和顶点连通度刻画二项边理想的深度
Depth of Binomial Edge Ideals in terms of Diameter and Vertex Connectivity
AI总结：
本文基于图的直径和顶点连通度等不变量，对满足深度上下界关系$L(G)+1=U(G)$的简单连通非完全图进行了结构分类，并计算了此类图二项边理想$S/J_G$的深度。
摘要：
设$G$为简单连通非完全图，$J_G$为其在多项式环$S$中的二项边理想。利用图的某些不变量（如$U(G)$），Banerjee和Núñez-Betancourt给出了$S/J_G$深度的上界，Rouzbahani Malayeri等人则给出了下界$L(G)$。Hibi和Saeedi Madani对满足$L(G)=U(G)$的图进行了结构分类。本文对满足$L(G)+1=U(G)$的图给出了结构分类，并计算了所有此类图$G$的$S/J_G$深度。
英文摘要：
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 $G$.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
