Frame Scaling by Graphs

TL;DR

This paper explores how to determine the scalability of frames in Euclidean spaces using graph theory, providing necessary conditions and analyzing special frame classes.

Contribution

It introduces a graph-based approach to test frame scalability and investigates specific classes of frames with this method.

Findings

Graph association helps verify frame scalability.

Necessary conditions for frame scalability are established.

Analysis of special frame classes using graphs.

Abstract

In this paper, we investigate the scalability of a given frame in $\mathbb{R}^n$ by using graphs. For each frame $\phi$ in $\mathbb{R}^n$, we associate a simple undirected graph $G(\phi)$ and use it to verify the scalability of $\phi$. We provide some necessary conditions to test the scalability of a given frame. Finally, we study the scalability of some special classes of frames by using graphs.