SHELLABILITY, VERTEX DECOMPOSABILITY, AND LEXICOGRAPHICAL PRODUCTS OF GRAPHS Academic Article uri icon

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abstract

  • We investigate when the independence complex of $G[H]$, the lexicographical product of two graphs $G$ and $H$, is either vertex decomposable or shellable. As an application, we construct an infinite family of graphs with the property that every graph in this family has the property that the independence complex of each graph is shellable, but not vertex decomposable.

publication date

  • January 1, 2017