In a finite simple undirected graph, a vertex is simplicial if its neighborhood is a clique. We say that, for k 2, a graph G = (VG, EG) is the k-simplicial power of a graph H = (V...
We consider the vertex-isoperimetric problem for cartesian powers of a graph G. A total order on the vertex set of G is called isoperimetric if the boundary of sets of a given siz...
We generalize the concept of a cycle from graphs to simplicial complexes. We show that a simplicial cycle is either a sequence of facets connected in the shape of a circle, or is ...
We consider a variety of connections between threshold graphs, shifted complexes, and simplicial complexes naturally formed from a graph. These graphical complexes include the inde...