Weakly distance-regular circulants, I

TL;DR

This paper classifies specific weakly distance-regular circulants and primitive cases using association schemes and Schur rings, advancing understanding of their algebraic structure and classification.

Contribution

It provides a classification of non-symmetric commutative association schemes and all weakly distance-regular circulants of a certain type, including primitive cases.

Findings

Classified certain non-symmetric commutative association schemes.

Determined all weakly distance-regular circulants of a specific arc type.

Provided classification of primitive weakly distance-regular circulants.

Abstract

We classify certain non-symmetric commutative association schemes. As an application, we determine all the weakly distance-regular circulants of one type of arcs by using Schur rings. We also give the classification of primitive weakly distance-regular circulants.