SOME COHEN-MACAULAY AND UNMIXED BINOMIAL EDGE IDEALS

Abstract

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.