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arXiv · 1505.02837

Independence complexes of well-covered circulant graphs

Jonathan Earl·Kevin N. Vander Meulen·Adam Van Tuyl
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Abstract

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.

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Jonathan Earl, Kevin N. Vander Meulen, Adam Van Tuyl. 2015-05-11. Independence complexes of well-covered circulant graphs. https://arxiv.org/abs/1505.02837

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