Semisymmetric graphs from polytopes

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. s: semisymmetric graphs, abstract regular and chiral polytopes. AMS Subject Classification (1991): Primary: 05C25. Secondary: 51M20. ∗Supported by the NSERC of Canada, grant 4818 †Supported by Ministry of Higher Education, Science and Technolgy of Slovenia grants P1-0294,J1-6062,L1-7230. ‡Supported by NSA-grant H98230-05-1-0027 §Supported by the NSERC of Canada, grant 8857 1 

• Type: Journal
• Year: 2007
• Where: JCT
• Authors: Barry Monson, Tomaz Pisanski, Egon Schulte, Asia Ivic Weiss
• Keywords: AMS Subject Classification, JCT 2007, Medial Layer Graph, Semisymmetric Trivalent Graphs