2-Dimensional vertex decomposable circulant graphs

Let G be the circulant graph Cn(S) with S ⊆ { 1, . . ., [n/2]} and let A be its independence complex. We describe the well-covered circulant graphs with 2-dimensional A, and construct an infinite family of vertex-decomposable circulant graphs within this family. Moreover, we show that if Cn(S) has a 2-dimensional vertex decomposable A, then it has a level Stanley-Reisner ring.