Please use this identifier to cite or link to this item: http://hdl.handle.net/10397/12424
Title: Some new trace formulas of tensors with applications in spectral hypergraph theory
Authors: Shao, JY
Qi, L 
Hu, S
Keywords: Eigenvalue
Hypergraph
Spectrum
Tensor
Trace
Issue Date: 2015
Publisher: Taylor & Francis
Source: Linear and multilinear algebra, 2015, v. 63, no. 5, p. 971-992 How to cite?
Journal: Linear and multilinear algebra 
Abstract: We give some graph theoretical formulas for the trace (Formula presented.) of a tensor (Formula presented.) which do not involve the differential operators and auxiliary matrix. As applications of these trace formulas in the study of the spectra of uniform hypergraphs, we give a characterization (in terms of the traces of the adjacency tensors) of the (Formula presented.) -uniform hypergraphs whose spectra are (Formula presented.) -symmetric, thus give an answer to a question raised in Cooper and Dutle [Linear Algebra Appl. 2012;436:3268–3292]. We generalize the results in Cooper and Dutle [Linear Algebra Appl. 2012;436:3268–3292, Theorem 4.2] and Hu and Qi [Discrete Appl. Math. 2014;169:140–151, Proposition 3.1] about the (Formula presented.) -symmetry of the spectrum of a (Formula presented.) -uniform hypergraph, and answer a question in Hu and Qi [Discrete Appl. Math. 2014;169:140–151] about the relation between the Laplacian and signless Laplacian spectra of a (Formula presented.) -uniform hypergraph when (Formula presented.) is odd. We also give a simplified proof of an expression for (Formula presented.) and discuss the expression for (Formula presented.).
URI: http://hdl.handle.net/10397/12424
ISSN: 0308-1087
EISSN: 1563-5139
DOI: 10.1080/03081087.2014.910208
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