Almost complete intersection binomial edge ideals and their Rees algebras

Let G be a simple graph on n vertices and JG denote the binomial edge ideal of in polynomial ring S=K[x1,…,xn,y1,…,yn]. In this article, we compute second graded Betti numbers JG, obtain minimal presentation it when is tree or unicyclic graph. We classify all graphs whose ideals are almost complete intersection, prove that they generated by d-sequence Rees algebra their Cohen-Macaulay. also an explicit description defining those ideals.