Abstract
We construct an infinite family{Γ n}n=5 of finite connected graphsΓ n that are multiple extensions of the well-known “extended grid” discovered in [1] (which is isomorphic toΓ 5). The graphsΓ n are locallyΓ n−1 forn > 5, and have the following property: the automorphism groupG(n) ofΓ n permutes transitively the maximal cliques ofΓ n (which aren-cliques) and the stabilizer of somen-cliqueπ ofΓ n inG(n) inducesΣ n on the vertices ofπ. Furthermore we show that the clique complexes of the graphsΓ n are simply connected.
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Meixner, T., Pasini, A. A family of multiply extended grids. Graphs and Combinatorics 12, 283–293 (1996). https://doi.org/10.1007/BF01858461
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DOI: https://doi.org/10.1007/BF01858461