2009/10/20 by Gabriela Araujo-Pardo, Gabriela Araujo‐Pardo, Maria Del Rio-Francos +11
Engineering · Mathematics · #05C25: 52B15 #51M20 #Advanced Measurement and Metrology Techniques #Combinatorics (math.CO) #FOS: Mathematics #Metric Geometry (math.MG) #math.CO #math.MG #msc:51M20 #msc:52B15
paper · pdf · doi:10.48550/arxiv.0910.3908
21 pages (European Journal of Combinatorics, to appear)
arxiv created 2009/10/20 · openalex publication_date 2009/10/20 · arxiv updated 2009/12/01 · openalex created_date 2024/04/11 · openalex updated_date 2026/07/28
The paper describes a construction of abstract polytopes from Cayley graphs of symmetric groups. Given any connected graph G with p vertices and q edges, we associate with G a Cayley graph of the symmetric group Sp and then construct a vertex-transitive simple polytope of rank q, called the graphicahedron, whose 1-skeleton (edge graph) is the Cayley graph. The graphicahedron of a graph G is a generalization of the well-known permutahedron; the latter is obtained when the graph is a path. We also discuss symmetry properties of the graphicahedron and determine its structure when G is small.