Shellability, vertex decomposability, and lexicographical products of graphs
Kevin N. Vander Meulen, Adam Van Tuyl · Libraries and Cultural Resources (University of Calgary) · 2015
In this note we describe when the independence complex of G[H], the lexicographical product of two graphs G and H, is either vertex decomposable or shellable. As an application, we show that there exists an infinite family of graphs whose independence complexes are shellable but not vertex decomposable.