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 wellknown classes of graphs and their products.
 Publication:

arXiv eprints
 Pub Date:
 January 2022
 DOI:
 10.48550/arXiv.2201.01640
 arXiv:
 arXiv:2201.01640
 Bibcode:
 2022arXiv220101640N
 Keywords:

 Mathematics  Combinatorics;
 Mathematics  Analysis of PDEs