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Operations Research Transactions >

2025 , Vol. 29 >Issue 4: 205 - 218

DOI: https://doi.org/10.15960/j.cnki.issn.1007-6093.2025.04.016

Research Article

On the upper bound of spectral radius of a class of nonnegative general-tensors and its applications

  • Yuan WANG ,
  • Zhongxun ZHU ,
  • Liansheng TAN ,
  • Yu YANG
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  • 1. College of Preparatory Education, South-Central Minzu University, Wuhan 430074, Hubei, China
    2. School of Computer Science, Central China Normal University, Wuhan 430079, Hubei, China
    3. Psychological Fitness Teaching and Research Center, Yunnan Police College, Kunming 650221, Yunnan, China

Received date: 2022-08-02

  Online published: 2025-12-11

Copyright

, 2025, All rights reserved. Unauthorized reproduction is prohibited.
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Abstract

According to the nonnegative tensors defined in Xu et al. (2016), we first obtain some combinatorial identities related on these tensors. Then we attain a sharp upper bound on the spectral radius of this type tensors and its corresponding extremal conditions by these combinatorial identities. As its applications, some sharp upper bounds on the spectral radius of general hypergraphs are deduced and their corresponding extremal structure are characterized.

Key words： nonnegative general-tensor; weakly irreducibletensor; spectral radius

Cite this article

Yuan WANG , Zhongxun ZHU , Liansheng TAN , Yu YANG . On the upper bound of spectral radius of a class of nonnegative general-tensors and its applications[J]. Operations Research Transactions, 2025 , 29(4) : 205 -218 . DOI: 10.15960/j.cnki.issn.1007-6093.2025.04.016

References

1 Lim L. Singular values and eigenvalues of tensors: A variational approach[C]//Proceedings of the 1st IEEE International Workshop on Computational Advances in Multi-Sensor Adaptive Processing, 2005, 1: 129-132.
2 Lim L. Foundations of numerical multilinear algebra: Decomposition and approximation of tensors[D]. Stanford: Stanford University, 2007.
3 Qi L . Eigenvalues of a real supersymmetric tensor[J]. Journal of Symbolic Computation, 2005, 40 (6): 1302- 1324.
4 Khan M , Fan Y . On the spectral radius of a class of non-odd-bipartite even uniform hypergraphs[J]. Linear Algebra and Its Applications, 2015, 480, 93- 106.
5 Yang Y , Yang Q . Further results for Perron-Frobenius theorem for nonnegative tensors[J]. SIAM Journal on Matrix Analysis and Applications, 2010, 31 (5): 2517- 2530.
6 Shao J . A general product of tensors with applications[J]. Linear Algebra and Its Applications, 2013, 439, 2350- 2366.
7 Brualdi R . Introductory Combinatorics[M]. Beijing: China Machine Press, 2002.
8 Hillar C , Lim L . Most tensor problems are NP-hard[J]. Journal of the ACM, 2013, 60 (6): 1- 39.
9 Badeau R , Boyer R . Fast multilinear singular value decomposition for structured tensors[J]. SIAM Journal on Matrix Analysis and Applications, 2008, 30 (3): 1008- 1021.
10 Jensen J , Helpern J , Ramani A , et al. Diffusional kurtosis imaging: The quantification of non-Gaussian water diffusion by means of magnetic resonance imaging[J]. Magnetic Resonance in Medicine, 2005, 53 (6): 1432- 1440.
11 Qi L , Luo Z . Tensor Analysis: Spectral Theory and Special Tensors[M]. SIAM Philadelphia: Society for Industrial and Applied Mathematics, 2017.
12 Xu C , Luo Z , Qi L , et al. {0, 1} completely positive tensors and multi-hypergraphs[J]. Linear Algebra and Its Applications, 2016, 510, 110- 123.
13 Chuan L , You L , Zhang X . A sharp upper bound on the spectral radius of a nonnegative k-uniform tensorand its applications to (directed) hypergraphs[J]. Journal of Inequalities and Applications, 2020, 2020 (1): 1- 16.
14 Banerjee A , Char A , Mondal B . Spectra of general hypergraphs[J]. Linear Algebra and Its Applications, 2017, 518, 14- 30.
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