A classification of Q-polynomial distance-regular graphs with girth 6Miklavič, Štefko (Avtor) distance-regular graphsQ-polynomial propertygirthLet Γ denote a Q-polynomial distance-regular graph with diameter D and valency k≥3. In [Homotopy in Q-polynomial distance-regular graphs, Discrete Math., {\bf 223} (2000), 189–206], H. Lewis showed that the girth of Γ is at most 6. In this paper we classify graphs that attain this upper bound. We show that Γ has girth 6 if and only if it is either isomorphic to the Odd graph on a set of cardinality 2D+1, or to a generalized hexagon of order (1,k−1).20252025-12-01 08:36:15Članek v reviji22155sl