Extended double covers of non-symmetric association schemes of class $2$

TL;DR

This paper introduces a method to construct non-symmetric association schemes of class 3 from those of class 2, extending the concept of Taylor graphs and relating to Pasechnik's doubling technique.

Contribution

It provides a novel construction method for non-symmetric association schemes of higher class, expanding the theoretical framework of association schemes.

Findings

Constructed non-symmetric association schemes of class 3 from class 2 schemes.

Extended the analogy of Taylor graphs to non-symmetric cases.

Discussed interactions with Pasechnik's doubling method.

Abstract

In this paper, we give a method to construct non-symmetric association schemes of class $3$ from non-symmetric association schemes of class $2$. This construction is a non-symmetric analogue of the construction of Taylor graphs as an antipodal double cover of a complete graph. We also mention how our construction interact with doubling introduced by Pasechnik.