2025/01/22 by Štefko Miklavič, Miklavič, Štefko
Mathematics · Engineering · #Finite Group Theory Research #Advanced Topics in Algebra #graph theory and CDMA systems
paper · doi:10.48550/arxiv.2501.12820
Let 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).