Frame Scaling by Graphs

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.