1. Frame graph.
- Author
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Abdollahi, Farshid and Najafi, Hashem
- Subjects
- *
GRAPH theory , *HILBERT space , *GEOMETRIC vertices , *LAPLACIAN matrices , *MATHEMATICAL sequences - Abstract
Let
be a finite-dimensional Hilbert space and be a finite frame for . For , we associate a simple graph denoted by and called frame graph, with all elements of as vertices, and two distinct vertices are adjacent when the inner product of them is nonzero. The associated graph is called a tight frame graph if the mentioned frame is tight. In this paper, we study some basic properties of and investigate the relation between the frame-theoretic properties of and the graph-theoretic properties of . For example, it is shown that trees on more than two vertices and cycles on more than five vertices are not tight frame graphs while complete graphs, complete graphs minus a single edge and the join of each graph with itself are tight frame graphs. [ABSTRACT FROM AUTHOR] - Published
- 2018
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