Semisymmetric Graphs from Polytopes
Barry Monson, Tomaz Pisanski, Egon Schulte, Asia Ivic Weiss
Abstract
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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