RESEARCH ARTICLE

Laplacian and signless Laplacian Z-eigenvalues of uniform hypergraphs

  • Changjiang BU ,
  • Yamin FAN ,
  • Jiang ZHOU
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  • College of Science, Harbin Engineering University, Harbin 150001, China

Received date: 12 Jan 2015

Accepted date: 16 Mar 2015

Published date: 17 May 2016

Copyright

2014 Higher Education Press and Springer-Verlag Berlin Heidelberg

Abstract

We show that a connected uniform hypergraph G is odd-bipartite if and only if G has the same Laplacian and signless Laplacian Z-eigenvalues. We obtain some bounds for the largest (signless) Laplacian Z-eigenvalue of a hypergraph. For a k-uniform hyperstar with d edges (2dk≥3), we show that its largest (signless) Laplacian Z-eigenvalue is d.

Cite this article

Changjiang BU , Yamin FAN , Jiang ZHOU . Laplacian and signless Laplacian Z-eigenvalues of uniform hypergraphs[J]. Frontiers of Mathematics in China, 2016 , 11(3) : 511 -520 . DOI: 10.1007/s11464-015-0467-x

1
Bu C, Zhou J, Wei Y. E-cospectral hypergraphs and some hypergraphs determined by their spectra. Linear Algebra Appl, 2014, 459: 397–403

DOI

2
Cooper J, Dutle A. Spectra of uniform hypergraphs. Linear Algebra Appl, 2012, 436: 3268–3292

DOI

3
Cooper J, Dutle A. Computing hypermatrix spectra with the Poisson product formula. Linear Multilinear Algebra, 2015, 63: 956–970

DOI

4
Cvetković D, Rowlinson P, Simić S. An Introduction to the Theory of Graph Spectra. Cambridge: Cambridge University Press, 2010

5
Hu S, Qi L. The eigenvectors associated with the zero eigenvalues of the Laplacian and signless Laplacian tensors of a uniform hypergraph. Discrete Appl Math, 2014, 169: 140–151

DOI

6
Hu S, Qi L, Xie J. The largest Laplacian and signless Laplacian H-eigenvalues of a uniform hypergraph. Linear Algebra Appl, 2015, 469: 1–27

DOI

7
Khan M, Fan Y. On the spectral radius of a class of non-odd-bipartite even uniform hypergraphs. arXiv: 1408.3303

8
Lim L H. Singular values and eigenvalues of tensors: a variational approach. In: Proceedings of the IEEE International Workshop on Computational Advances in Multisensor Adaptive Processing. 2005, 129–132

9
Pearson K, Zhang T. On spectral hypergraph theory of the adjacency tensor. Graphs Combin, 2014, 30: 1233–1248

DOI

10
Qi L. Eigenvalues of a real supersymmetric tensor. J Symbolic Comput, 2005, 40: 1302–1324

DOI

11
Qi L. H+-eigenvalues of Laplacian and signless Laplacian tensors. Commun Math Sci, 2014, 12: 1045–1064

DOI

12
Shao J. A general product of tensors with applications. Linear Algebra Appl, 2013, 439: 2350–2366

DOI

13
Shao J, Qi L, Hu S. Some new trace formulas of tensors with applications in spectral hypergraph theory. Linear Multilinear Algebra, 2015, 63: 971–992

DOI

14
Shao J, Shan H, Wu B. Some spectral properties and characterizations of connected odd-bipartite uniform hypergraphs. Linear Multilinear Algebra, DOI: 10.1080/03081087.2015.1009061

DOI

15
Song Y, Qi L. Spectral properties of positively homogeneous operators induced by higher order tensors. SIAM J Matrix Anal Appl, 2013, 34: 1581–1595

DOI

16
Xie J, Chang A. On the Z-eigenvalues of the adjacency tensors for uniform hypergraphs. Linear Algebra Appl, 2013, 439: 2195–2204

DOI

17
Zhou J, Sun L, Wang W, Bu C. Some spectral properties of uniform hypergraphs. Electron J Combin, 2014, 21: P4.24

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