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m, argest adjacency, signless Laplacian, and Laplacian H-eigenvalues of loose paths

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Frontiers of Mathematics in China 2016年第3期11卷 623-645页

作者： Junjie YUE Liping ZHANG Mei LU Department of Mathematical Sciences Tsinghua University Beijing 100084 China State Key Laboratory of Space Weather Chinese Academy of Sciences Beijing 100910 China

We investigate k-uniform loose paths. We show that the largest H- eigenvalues of their adjacency tensors, Laplacian tensors, and signless Laplacian tensors are computable. For a k-uniform loose path with length l≥ 3, we show that the largest H-eigenvalue of its adjacency tensor is （（1 ＋ √-5）/2）2/k when = 3 and ）λ（A） = 31/k when g = 4, respectively. For the case of l ≥ 5, we tighten the existing upper bound 2. We also show that the largest H-eigenvalue of its signless Laplacian tensor lies in the interval （2, 3） when l≥ 5. Finally, we investigate the largest H-eigenvalue of its Laplacian tensor when k is even and we tighten the upper bound 4.

关键词： H-eigenvalue hypergraph adjacency tensor signless Laplaciantensor Laplacian tensor loose path

The Linear Unicyclic Hypergraph with the Second or Third Largest Spectral Radius

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Acta Mathematica Sinica,English Series 2020年第10期36卷 1140-1150页

作者： Chao DING Yi Zheng FAN Jiang Chao WAN School of Mathematics and Physics Anqing Normal UniversityAnqing 246133P.R.China School of Mathematical Sciences Anhui UniversityHefei 230601P.R.China

The spectral radius of a uniform hypergraph is defined to be that of the adjacency tensor of the *** is known that the unique unicyclic hypergraph with the largest spectral radius is a nonlinear hypergraph,and the unique linear unicyclic hypergraph with the largest spectral radius is a power *** this paper we determine the unique linear unicyclic hypergraph with the second or third largest spectral radius,where the former hypergraph is a power hypergraph and the latter hypergraph is a non-power hypergraph.

关键词： Linear unicyclic hypergraph adjacency tensor spectral radius weighted incident matrix

Largest H-eigenvalue of uniform s-hypertrees

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Frontiers of Mathematics in China 2018年第2期13卷 301-312页

作者： Yuan HOU An CHANG Lei ZHANG Center for Discrete Mathematics and Theoretical Computer Science Fuzhou University Puzhou 350000 China Department of Computer Engineering Fuzhou University Zhicheng College Fuzhou 350000 China

The k-uniform s-hypertree G = （V, E） is an s-hypergraph, where 1 ≤ s ≤ k - 1, and there exists a host tree T with vertex set V such that each edge of G induces a connected subtree of T. In this paper, some properties of uniform s-hypertrees are establised, as well as the upper and lower bounds on the largest H-eigenvalue of the adjacency tensor of k-uniform s-hypertrees in terms of the maximal degree A. Moreover, we also show that the gap between the maximum and the minimum values of the largest H-eigenvalue of k-uniform s-hypertrees is just （△S/k）.

关键词： Largest H-eigenvalue spectral radius adjacency tensor hypertree

Ordering uniform supertrees by their spectral radii

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Frontiers of Mathematics in China 2017年第6期12卷 1393-1408页

作者： Xiying YUAN Xuelian SI Li ZHANG Department of Mathematics Shanghai University Shanghai 200444 China Sclool of Statistics and Mathematics Shanghai FinanceUniversityShanghai 201209 China

A supertree is a connected and acyclic hypergraph. For a hypergraph H, the maximal modulus of the eigenvalues of its adjacency tensor is called the spectral radius of H. By applying the operation of moving edges on hypergraphs and the weighted incidence matrix method, we determine the ninth and the tenth k-uniform supertrees with the largest spectral radii among all k-uniform supertrees on n vertices, which extends the known result.

关键词： Uniform hypergraph adjacency tensor uniform supertree spectral radius

The adjacency and Signless Laplacian Spectra of Cored Hypergraphs and Power Hypergraphs

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Journal of the Operations Research Society of China 2017年第1期5卷 27-43页

作者： Jun-Jie Yue Li-Ping Zhang Mei Lu Li-Qun Qi Department of Mathematical Sciences Tsinghua UniversityBeijing 100084China State Key Laboratory of Space Weather Chinese Academy of SciencesBeijing 100910China Department of Applied Mathematics The Hong Kong Polytechnic UniversityHong KongChina

In this paper,we study the adjacency and signless Laplacian tensors of cored hypergraphs and power *** investigate the properties of their adjacency and signless Laplacian ***,we find out the largest H-eigenvalues of adjacency and signless Laplacian tensors for uniform *** also compute the H-spectra of sunflowers and some numerical results are reported for the H-spectra.

关键词： H-eigenvalue Hypergraph adjacency tensor Signless Laplacian tensor Sunflower Squid