We discuss monotone dihedral graph properties, which are graph complexes on [n]that are invariant under the natural action of the dihedral group D n . More precisely, identify the corners of a regular n-gon with the vertices 1,…, n arranged in clockwise direction. Representing a given edge ij with the open line segment between the points representing i and j, we obtain the polygon representation of a graph. The natural action of D n on this graph is simply the action induced by the natural action of D n on the n—gon.
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© 2008 Springer-Verlag Berlin Heidelberg
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(2008). Dihedral Graph Properties. In: Simplicial Complexes of Graphs. Lecture Notes in Mathematics, vol 1928. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-75859-4_8
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DOI: https://doi.org/10.1007/978-3-540-75859-4_8
Publisher Name: Springer, Berlin, Heidelberg
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