  In this article, we compute the regularity of Rees algebra of binomial edge
ideals of closed graphs. We obtain a lower bound for the regularity of Rees
algebra of binomial edge ideals. We also study some algebraic properties of the
Rees algebra and special fiber ring of binomial edge ideals of closed graphs
via algebraic properties of their initial algebra and Sagbi basis theory. We
obtain an upper bound for the regularity of the special fiber ring of binomial
edge ideals of closed graphs.
