Spectral radius of uniform hypergraphs and degree sequences

Abstract

We present several upper bounds for the adjacency and signless Laplacian spectral radii of uniform hypergraphs in terms of degree sequences.

Keywords

Spectral radius / uniform hypergraph / degree sequence

References

[1] ChangK-C, QiL, ZhangT. A survey on the spectral theory of nonnegative tensors.Numer Linear Algebra Appl, 2013, 20: 891–912

[2] CooperJ, DutleA. Spectra of uniform hypergraphs. Linear Algebra Appl,2012, 436: 3268–3292

[3] FriedlandS, GaubertS, HanL. Perron-Frobenius theorems for nonnegative multilinear forms and extension.Linear Algebra Appl, 2013, 438: 738–749

[4] KhanM, FanY-Z. On the spectral radius of a class of non-odd-bipartite even uniform hypergraphs.Linear Algebra Appl, 2015, 480: 93–106

[5] KhanM, FanY-Z, TanY-Y. The H-spectra of a class of generalized power hypergraphs.Discrete Math, 2016, 339: 1682–1689

[6] LiC, ChenZ, LiY. A new eigenvalue inclusion set for tensors and its applications.Linear Algebra Appl,2015, 481: 36–53

[7] LiH-H, ShaoJ-Y, QiL. The extremal spectral radii of k-uniform supertrees.J Comb Optim, 2016, 32: 741–764

[8] LinH-Y, ZhouB, MoB. Upper bounds for H- and Z-spectral radii of uniform hypergraphs.Linear Algebra Appl, 2016, 510: 205–211

[9] LovászL, PelikánJ, VesztergombiK. Discrete Mathematics: Elementary and Beyond.Undergrad Texts Math. New York: Springer-Verlag, 2003

[10] PearsonK, ZhangT. On spectral hypergraph theory of the adjacency tensor.Graphs Combin,2014, 30: 1233–1248

[11] QiL. Eigenvalues of a real supersymmetric tensor.J Symbol Comput,2005, 40: 1302–1324

[12] QiL. H-eigenvalues of Laplacian and signless Laplacian tensors.Commun Math Sci,2014, 12: 1045–1064

[13] QiL, ShaoJ-Y, WangQ. Regular uniform hypergraphs, s-cycles, s-paths and their largest Laplacian eigenvalues.Linear Algebra Appl,2014, 443: 215–227

[14] ShaoJ-Y. A general product of tensors with applications.Linear Algebra Appl,2012, 439: 2350–2366

[15] YangY, YangQ. Further results for Perron-Frobenius theorem for nonnegative tensors.SIAM J Matrix Anal Appl, 2010, 31: 2517–2530

[16] YuanX, QiL, ShaoJ-Y. The proof of a conjecture on largest Laplacian and signless Laplacian H-eigenvalues of uniform hypergraphs.Linear Algebra Appl, 2016, 490: 18–30

[17] YuanX, ShaoJ-Y, ShanH-Y. Ordering of some uniform supertrees with larger spectral radii.Linear Algebra Appl, 2016, 495: 206–222

[18] YuanX, ZhangM, LuM. Some upper bounds on the eigenvalues of uniform hypergraphs.Linear Algebra Appl, 2015, 484: 540–549

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Higher Education Press and Springer-Verlag GmbH Germany