Level and pseudo-Gorenstein binomial edge ideals (Q6114008)

Let \(G\) be a simple graph with \(n\) vertices. The authors study the binomial edge ideal of \(G\), denoted by \(J_G.\) It is proved that level binomial edge ideals with regularity \(2\) are cones and that the same is true for pseudo-Gorenstein binomial edge ideals with regularity \(3.\) In the case of bipartite graphs, the level or pseudo-Gorenstein binomial edge ideals are characterized. A list of all level and pseudo-Gorenstein binomial edge ideals with at most \(12\) vertices is provided. Two open questions are presented.