The Graphicahedron

Details The Graphicahedron The Graphicahedron

2009-10-20

arxiv.org/abs/0910.3908v1

Mathematics

Combinatorics

21 pages (European Journal of Combinatorics, to appear)

Scientific paper

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 S_p 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.

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