Abstract: Kneser graph is a very important kind of graph. Many problems related to counting and computing sets can be transformed into the problems in this kind of graph. It is widely used in computer science, graph theory, and topology. In the report, in algebraic combination respect, the combinatorial algebraic structures of Kneser graphs and their induced subgraphs, including Schrijver graphs and interlacing graphs were studied, and their vertex decomposability and Cohen-Macaulay properties were fully characterized.