English

Characterization of some classes of graphs and their products as frame graph

Combinatorics 2022-01-06 v1 Analysis of PDEs

Abstract

To each finite frame φ\varphi in an inner product space H\mathcal{H} we associate a simple graph G(φ)G(\varphi), called {\it frame graph}, with the vectors of the frame as vertices and there is an edge between vertices ff and gg provided that f,g0\langle f, g\rangle \neq 0 [1]. In this paper the relation between the order of G(φ)G(\varphi) and the dimension of H\mathcal{H} is investigated for some well-known classes of graphs and their products.

Keywords

Cite

@article{arxiv.2201.01640,
  title  = {Characterization of some classes of graphs and their products as frame graph},
  author = {H. Najafi and F. Abdollahi},
  journal= {arXiv preprint arXiv:2201.01640},
  year   = {2022}
}