INTERSECTION GRAPH OF A SIMPLICIAL COMPLEX

Abstract

In this note, firstly 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 investigate some properties of this graph and simplicial complexes. Moreover, we apply this graph for finding 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.