Primitive weakly distance-regular circulant digraphs

TL;DR

This paper classifies specific non-symmetric association schemes and identifies all primitive weakly distance-regular circulant digraphs, advancing understanding of their structure and classification.

Contribution

It provides a complete classification of primitive weakly distance-regular circulant digraphs, a previously unresolved problem in algebraic graph theory.

Findings

All primitive weakly distance-regular circulant digraphs are classified.

The classification relies on the analysis of non-symmetric commutative association schemes.

The results contribute to the broader understanding of algebraic properties of circulant digraphs.

Abstract

We classify certain non-symmetric commutative association schemes. As an application, we determine all the primitive weakly distance-regular circulant digraphs.