Let G be a finite simple graph on n vertices and JG denote the corresponding binomial edge
ideal in S= K [x 1,…, xn, y 1,…, yn]. We compute the Castelnuovo-Mumford regularity of S/JG …

We study unmixed and Cohen-Macaulay properties of the binomial edge ideal of some
classes of graphs. We compute the depth of the binomial edge ideal of a generalized block …

We prove that the regularity of binomial edge ideals of graphs obtained by gluing two graphs
at a free vertex is the sum of the regularity of individual graphs. As a consequence, we …

In this paper we prove the conjectured upper bound for Castelnuovo–Mumford regularity of
binomial edge ideals posed in 23, in the case of chordal graphs. Indeed, we show that the …

We characterize all graphs whose binomial edge ideals have pure resolutions. Moreover,
we introduce a new switching of graphs which does not change some algebraic invariants of …

arXiv:1808.06374v1 [math.AC] 20 Aug 2018 Page 1 arXiv:1808.06374v1 [math.AC] 20 Aug
2018 AN UPPER BOUND FOR THE REGULARITY OF BINOMIAL EDGE IDEALS OF …

arXiv:2209.01201v3 [math.AC] 13 Jul 2023 Page 1 arXiv:2209.01201v3 [math.AC] 13 Jul 2023
RECENT RESULTS ON HOMOLOGICAL PROPERTIES OF BINOMIAL EDGE IDEAL OF …

A graph is closed when its vertices have a labeling by $[n] $ such that the binomial edge
ideal $ J_G $ has a quadratic Gr\"{o} bner basis with respect to the lexicographic order …

In this thesis, we study the binomial edge ideals associated with graphs. We review their
reduced Gröber basis and minimal primary decompositions. Moreover, we also give an …