2-dimensional vertex decomposable circulant graphs

Abstract

Let $G$ be the circulant graph $C_n(S)$ with $S\subseteq \{1,\dots ,\lfloor \frac{n}{2}\rfloor \}$ and let $\Delta$ be its independence complex. We describe the well-covered circulant graphs with 2-dimensional $\Delta$ and construct an infinite family of vertex-decomposable circulant graphs within this family.