2015/05/11 by Earl, Jonathan, Meulen, Kevin N. Vander, Van Tuyl, Adam
#05C75 #05E45 #13F55 #Combinatorics (math.CO) #Commutative Algebra (math.AC) #FOS: Mathematics
paper · doi:10.48550/arxiv.1505.02837
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) structure. We also provide a table of all well-covered circulant graphs on 16 or less vertices, and for each such graph, determine if it is vertex decomposable, shellable, Cohen-Macaulay, and/or Buchsbaum. A highlight of this search is an example of a graph whose independence complex is shellable but not vertex decomposable.