In this note, rstly we introduce the intersection graph G() of a simplicial complex , as a graph whose vertices are all facets of and two distinct vertices are adjacent if they have non-empty intersection. We inves- tigate some properties of this graph and simplicial complexes. Moreover, we apply this graph for nding a couple of upper and lower bounds for the vertex covering number of . Also, we introduce and study the intersection ideal of a simplicial complex.
