Mutually orthogonal Sudoku Latin squares and their graphs

TL;DR

This paper introduces a graph structure based on mutually orthogonal Sudoku Latin squares, determines its spectra from finite fields, and uses eigenvalues to distinguish non-isomorphic squares, advancing combinatorial and graph-theoretic understanding.

Contribution

It presents a novel graph construction from Sudoku Latin squares, explicitly computes spectra from finite fields, and applies eigenvalues to differentiate non-isomorphic cases.

Findings

Spectra of graphs from finite fields are explicitly determined.

Eigenvalues can distinguish non-isomorphic Sudoku Latin squares.

New graph-theoretic tools for analyzing Sudoku Latin squares.

Abstract

We introduce a graph attached to mutually orthogonal Sudoku Latin squares. The spectra of the graphs obtained from finite fields are explicitly determined. As a corollary, we then use the eigenvalues to distinguish non-isomorphic Sudoku Latin squares.