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The PUMP Journal of Undergraduate Research
Article . 2021 . Peer-reviewed
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Tight Frame Graphs Arising as Line Graphs

Tight frame graphs arising as line graphs
descriptionPublicationkeyboard_double_arrow_right Article , Preprint 20 Jan 2021Embargo end date: 01 Jan 2020Publisher:California State University, Office of the ChancellorJournal:The PUMP Journal of Undergraduate Research, volume 4, pages 1-19 (issn: 2765-8724, eissn: 2576-3725, Copyright policy )
Authors: Furst, Veronika; Grotts, Howard;

doi: 10.46787/pump.v4i0.2415 , 10.48550/arxiv.2007.08673

arXiv: 2007.08673

Tight Frame Graphs Arising as Line Graphs

Abstract

Dual multiplicity graphs are those simple, undirected graphs that have a weighted Hermitian adjacency matrix with only two distinct eigenvalues. From the point of view of frame theory, their characterization can be restated as which graphs have a representation by a tight frame. In this paper, we classify certain line graphs that are tight frame graphs and improve a previous result on the embedding of frame graphs in tight frame graphs.

Related Organizations
Keywords

Eigenvalues, singular values, and eigenvectors, Graphs and linear algebra (matrices, eigenvalues, etc.), Graph operations (line graphs, products, etc.), General harmonic expansions, frames, dual multiplicity graph, line graph, tight frame graph, FOS: Mathematics, Mathematics - Combinatorics, 05C50, 15A18, 42C15, Gram matrix, Combinatorics (math.CO), Laplacian matrix

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
1
Average
Average
Average
Green
hybrid