Semisymmetric Graphs from Polytopes

Details Semisymmetric Graphs from Polytopes Semisymmetric Graphs from Polytopes

2006-06-19

arxiv.org/abs/math/0606469v1

Mathematics

Combinatorics

18 pages (to appear in Journal Combinatorial Theory, Series A)

Scientific paper

Every finite, self-dual, regular (or chiral) 4-polytope of type {3,q,3} has a trivalent 3-transitive (or 2-transitive) medial layer graph. Here, by dropping self-duality, we obtain a construction for semisymmetric trivalent graphs (which are edge- but not vertex-transitive). In particular, the Gray graph arises as the medial layer graph of a certain universal locally toroidal regular 4-polytope.

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