There are only finitely many distance-regular graphs of fixed valency greater than two

TL;DR

This paper proves the Bannai-Ito conjecture, establishing that only finitely many distance-regular graphs exist for each fixed valency greater than two, thus advancing understanding in algebraic graph theory.

Contribution

The paper confirms the Bannai-Ito conjecture, showing the finiteness of distance-regular graphs with fixed valency greater than two, a significant theoretical result.

Findings

Proves the Bannai-Ito conjecture

Finiteness of distance-regular graphs for fixed valency

Advances algebraic graph theory understanding

Abstract

In this paper we prove the Bannai-Ito conjecture, namely that there are only finitely many distance-regular graphs of fixed valency greater than two.