There are only finitely many regular near polygons and geodetic distance-regular graphs with fixed valency

Abstract

In their 1984 book "Algebraic Combinatorics I: Association Schemes'', Bannai and Ito conjectured that there are only finitely many distance-regular graphs with fixed valency at least three. In a series of papers they showed that their conjecture holds for the class of bipartite distance-regular graphs. In this paper we prove that the Bannai-Ito conjecture also holds for the more general class of regular near polygons, and for the class of geodetic distance-regular graphs.