Characterization of some classes of graphs and their products as frame graph
Abstract
To each finite frame $\varphi$ in an inner product space $\mathcal{H}$ we associate a simple graph $G(\varphi)$, called {\it frame graph}, with the vectors of the frame as vertices and there is an edge between vertices $f$ and $g$ provided that $\langle f, g\rangle \neq 0$ [1]. In this paper the relation between the order of $G(\varphi)$ and the dimension of $\mathcal{H}$ is investigated for some well-known classes of graphs and their products.
- Publication:
-
arXiv e-prints
- Pub Date:
- January 2022
- DOI:
- 10.48550/arXiv.2201.01640
- arXiv:
- arXiv:2201.01640
- Bibcode:
- 2022arXiv220101640N
- Keywords:
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- Mathematics - Combinatorics;
- Mathematics - Analysis of PDEs