Yet another look at the Gray graph [Elektronski vir]
Pisanski, Tomaž
The Gray graph is the smallest trivalent semisymmetric graph; it has 54 vertices. We present three descriptions of this remarkable graph and establish their equivalence. The construction readily ...generalizes in order to produce a series of semisymmetric graphs of arbitrary valence ▫$n > 2$▫. Also, this implies the existence of geometric triangle-free point-transitive, line-transitive, flag-transitive non self-dual configurations of type ▫$(n_n^n$▫, for any ▫$n > 2$▫. These graphs have been studied already by R. Foster and I. Bouwer. The Gray graph appears as the medial layer graph of a regular 4-polytope. The combinatorial structure of this polytope is explained in detail. A relationship between the Gray graph and the Pappus graph is presented.
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