Properties of SSC of Wheel Graphs

Abstract

Let G be a finite graph with vertex set V and edge set E. A graph complex on G is an abstract simplicial complex consisting of subsets of E. In particular, we may interpret such a complex as a family of subgraphs of G. The subject of the thesis is the Properties of SSC of Wheel Graphs, the emphasis being placed on homology, connectivity degree, Cohen-Macaulayness, and Vertex Decomposition. Let ∆ be a pure simplicial complex on n vertices having dimension d and codimension c = n−d −1 in the simplex. Terai and Yoshida proved that if the number of facets of ∆ is at least