  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 graph. We also characterize all generalized block graphs
whose binomial edge ideals are Cohen-Macaulay and unmixed. So that we
generalize the results of Ene, Herzog and Hibi on block graphs. Moreover, we
study unmixedness and Cohen-Macaulayness of the binomial edge ideal of some
graph products such as the join and corona of two graphs with respect to the
original graphs'.
