Local distributions for eigenfunctions and for perfect colorings of q-ary hypercube

TL;DR

This paper investigates the local distributions of eigenfunctions and perfect colorings in q-ary hypercube graphs, establishing their interdependence across orthogonal faces and contributing to spectral graph theory.

Contribution

It introduces new interdependence results for local distributions of eigenfunctions and perfect colorings in q-ary hypercubes, expanding understanding of their structural properties.

Findings

Interdependence of local distributions in orthogonal faces

Analogous results for perfect colorings

Advances in spectral analysis of q-ary hypercubes

Abstract

Under study are the eigenfunctions and perfect colorings of the graph of $n$-dimensional $q$-ary Hamming space. We obtain the interdependence of local distributions of an eigenfunction in two orthogonal faces. We prove also an analogous result for perfect colorings.