Tight Frame Graphs Arising as Line Graphs

zbMath1462.05221arXiv2007.08673MaRDI QIDQ4987379

Veronika Furst, Howard Grotts

Publication date: 3 May 2021

Full work available at URL: https://arxiv.org/abs/2007.08673

zbMATH Keywords

line graphLaplacian matrixGram matrixdual multiplicity graphtight frame graph

Mathematics Subject Classification ID

Graphs and linear algebra (matrices, eigenvalues, etc.) (05C50) Eigenvalues, singular values, and eigenvectors (15A18) General harmonic expansions, frames (42C15) Graph operations (line graphs, products, etc.) (05C76)

Related Items (1)

Regular graphs of degree at most four that allow two distinct eigenvalues

Cites Work

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• The nowhere-zero eigenbasis problem for a graph
• Zero forcing parameters and minimum rank problems
• An introduction to finite tight frames
• The inverse eigenvalue problem of a graph: multiplicities and minors
• Undirected graphs of Hermitian matrices that admit only two distinct eigenvalues
• Every Hilbert space frame has a Naimark complement
• Achievable multiplicity partitions in the inverse eigenvalue problem of a graph
• Zero forcing sets and the minimum rank of graphs
• Positive semidefinite maximum nullity and zero forcing number
• On the Shannon capacity of a graph
• Optimization Methods for Frame Conditioning and Application to Graph Laplacian Scaling
• Frame graph
• Introduction to Finite Frame Theory
• Applications of analysis to the determination of the minimum number of distinct eigenvalues of a graph
• On the Line Graph of the Complete Bipartite Graph
• Characterizations of derived graphs
• Minimum number of distinct eigenvalues of graphs

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