Independence Complexes of Well-Covered Circulant Graphs

We study the independence complexes of families of well-covered circulant graphs discovered by Boros–Gurvich–Milanič, Brown–Hoshino, and Moussi. Because these graphs are well-covered, their independence complexes are pure simplicial complexes. We determine when these pure complexes have extra combinatorial (e.g., vertex decomposable, shellable) or topological (e.g., Cohen–Macaulay, Buchsbaum) properties. We also provide a table of all …