Equitable partitions of Latin-square graphs

TL;DR

This paper classifies equitable partitions of Latin-square graphs based on the eigenvalues of their quotient matrices, providing a comprehensive understanding of their structure.

Contribution

It offers a complete classification of equitable partitions of Latin-square graphs with quotient matrices lacking the eigenvalue -3.

Findings

Classified equitable partitions without eigenvalue -3

Identified structural properties of Latin-square graph partitions

Enhanced understanding of graph symmetry and eigenvalue constraints

Abstract

We study equitable partitions of Latin-square graphs, and give a complete classification of those whose quotient matrix does not have an eigenvalue $-3$.