Some new trace formulas of tensors with applications in spectral hypergraph theory

DOI10.1080/03081087.2014.910208zbMath1310.15042arXiv1307.5690OpenAlexW2074140319MaRDI QIDQ5175373

Liqun Qi, Jia-yu Shao, Sheng-Long Hu

Publication date: 20 February 2015

Published in: Linear and Multilinear Algebra (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1307.5690

zbMATH Keywords

tensorhypergrapheigenvaluespectrumtraceLaplacian

Mathematics Subject Classification ID

Hypergraphs (05C65) Determinants, permanents, traces, other special matrix functions (15A15) Eigenvalues, singular values, and eigenvectors (15A18) Multilinear algebra, tensor calculus (15A69)

Related Items (24)

Spectral moments of hypertrees and their applications ⋮ Applications of the Harary-Sachs theorem for hypergraphs ⋮ \(\mathrm{P}\)-tensors, \(\mathrm{P}_0\)-tensors, and their applications ⋮ The cyclic index of adjacency tensor of generalized power hypergraphs ⋮ A combinatorial method for computing characteristic polynomials of starlike hypergraphs ⋮ Estrada index and subgraph centrality of hypergraphs via tensors ⋮ Characteristic polynomial and higher order traces of third order three dimensional tensors ⋮ The characteristic polynomials of uniform double hyperstars and uniform hypertriangles ⋮ The trace and Estrada index of uniform hypergraphs with cut vertices ⋮ The high order spectrum of a graph and its applications in graph colouring and clique counting ⋮ Symmetry of eigenvalues of Sylvester matrices and tensors ⋮ On spectral theory of a k-uniform directed hypergraph ⋮ On a relationship between the characteristic and matching polynomials of a uniform hypertree ⋮ The eigenvectors associated with the zero eigenvalues of the Laplacian and signless Laplacian tensors of a uniform hypergraph ⋮ A reduction formula for the characteristic polynomial of hypergraph with pendant edges ⋮ The stabilizing index and cyclic index of the coalescence and Cartesian product of uniform hypergraphs ⋮ Hypergraph characterizations of copositive tensors ⋮ Laplacian and signless Laplacian Z-eigenvalues of uniform hypergraphs ⋮ A Harary-Sachs theorem for hypergraphs ⋮ Some characterizations of \(M\)-tensors via digraphs ⋮ Relationships between Brauer-type eigenvalue inclusion sets and a Brualdi-type eigenvalue inclusion set for tensors ⋮ Spectral directed hypergraph theory via tensors ⋮ The spectral symmetry of weakly irreducible nonnegative tensors and connected hypergraphs ⋮ Brualdi-type eigenvalue inclusion sets of tensors

Cites Work

• Unnamed Item
• Spectra of uniform hypergraphs
• Analogue of the identity Log Det = Trace Log for resultants
• On determinants and eigenvalue theory of tensors
• Cored hypergraphs, power hypergraphs and their Laplacian H-eigenvalues
• The eigenvectors associated with the zero eigenvalues of the Laplacian and signless Laplacian tensors of a uniform hypergraph
• Eigenvalues of a real supersymmetric tensor
• On eigenvalue problems of real symmetric tensors

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