Some adjacency-invariant spaces on products of short cycles

TL;DR

This paper investigates adjacency-invariant function spaces on product graphs of cyclic groups, with applications to spatio-spectral limiting, extending concepts analogous to time and band limiting.

Contribution

It introduces new adjacency-invariant spaces on product graphs of small cyclic groups and explores their application to spatio-spectral limiting problems.

Findings

Defined new adjacency-invariant function spaces

Analyzed properties of these spaces on specific product graphs

Connected the theory to spatio-spectral limiting applications

Abstract

We study certain spaces of vertex functions on the Cayley graphs corresponding to N-fold products of the group of integers modulo m, where m=3, 4, or 5, that are invariant under the adjacency operator that maps a value at a given vertex to each of its neighbors. An application to spatio-spectral limiting, an analogue of time and band limiting, is also discussed.