Shellability of Polyhedral Joins of Simplicial Complexes and Its Application to Graph Theory

We investigate the shellability of polyhedral join $\mathcal{Z}^*_M (K, L)$ simplicial complexes $K, M$ and a subcomplex $L \subset K$. give sufficient conditions necessary on $(K, for being shellable. In particular, we show that some pairs L)$, becomes shellable regardless whether $M$ is or not. Polyhedral joins can be applied to graph theory as independence complex certain generalized version lexicographic products graphs which define in this paper. The obtained from two $G, H$ by attaching one copy $H$ each vertex $G$ special case product result applying above results.