Extremal Betti numbers of some Cohen-Macaulay binomial edge ideals

We provide the regularity and the Cohen-Macaulay type of binomial edge ideals of Cohen-Macaulay cones, and we show the extremal Betti numbers of some classes of Cohen-Macaulay binomial edge ideals: Cohen-Macaulay bipartite and fan graphs. In addition, we compute the Hilbert-Poincar'e series of the binomial edge ideals of some Cohen-Macaulay bipartite graphs.