Frontiers of Mathematics in China >
Spectral radius of uniform hypergraphs and degree sequences
Received date: 30 Sep 2016
Accepted date: 29 Dec 2016
Published date: 27 Nov 2017
Copyright
We present several upper bounds for the adjacency and signless Laplacian spectral radii of uniform hypergraphs in terms of degree sequences.
Key words: Spectral radius; uniform hypergraph; degree sequence
Dongmei CHEN , Zhibing CHEN , Xiao-Dong ZHANG . Spectral radius of uniform hypergraphs and degree sequences[J]. Frontiers of Mathematics in China, 2017 , 12(6) : 1279 -1288 . DOI: 10.1007/s11464-017-0626-3
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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