Distance-regular graphs, the subconstituent algebra, and the $Q$-polynomial property

TL;DR

This survey provides an introductory overview of distance-regular graphs, focusing on the subconstituent algebra and the $Q$-polynomial property, essential concepts in algebraic graph theory.

Contribution

It offers a comprehensive tutorial on the fundamental aspects of distance-regular graphs, highlighting the significance of the subconstituent algebra and the $Q$-polynomial property.

Findings

Clarifies the structure of distance-regular graphs

Explains the role of the subconstituent algebra

Details the importance of the $Q$-polynomial property

Abstract

This survey paper contains a tutorial introduction to distance-regular graphs, with an emphasis on the subconstituent algebra and the $Q$-polynomial property.