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spectral radius of uniform hypergraphs and degree sequences

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Frontiers of Mathematics in China 2017年第6期12卷 1279-1288页

作者： Dongmei CHEN Zhibing CHEN Xiao-Dong ZHANG College of Mathematics and Statistics Shenzhen University Shenzhen 518060 China School of Mathematical Sciences MOE-LSC and SHL-MAC Shanghai Jiao Tong University Shanghai 200240 China

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

关键词： spectral radius uniform hypergraph degree sequence

Berry-Esseen bounds and moderate deviations for the norm, entries and spectral radius of products of positive random matrices

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Science China Mathematics 2024年第3期67卷 627-646页

作者： Hui Xiao Ion Grama Quansheng Liu Institut fur Mathematik und Angewandte Informatik Universitat HildesheimHildesheim 31141Germany Academy of Mathematics and Systems Science Chinese Academy of SciencesBeijing 100190China LMBA Universite Bretagne SudCNRS UMR 6205Vannes F-56000France

Let(g_(n))_(n≥1) be a sequence of independent and identically distributed positive random d×d matrices and consider the matrix product G_(n)=g_(n)…g_1.Under suitable conditions,we establish the Berry-Esseen bounds on the rate of convergence in the central limit theorem and Cramer-type moderate deviation expansions,for any matrix norm ‖G_(n)‖ of G_(n),its entries G_(n)^(i,j) and its spectral radius ρ(G_(n)).Extended versions of their joint law with the direction of the random walk G_(n)x are also established,where x is a starting point in the unit sphere of R~d.

关键词： Berry-Esseen bound Cramér-type moderate deviation product of random matrices operator norm entry spectral radius

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On the Distance Signless Laplacian spectral radius of Bicyclic Graphs

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Journal of Mathematical Research with Applications 2023年第3期43卷 289-302页

作者： Nannan XU Aimei YU School of Mathematics and Stastics Beijing Jiaotong University

The distance signless Laplacian matrix of a connected graph G is defined as Q(G)=Tr(G)+D(G), where Tr(G) is the diagonal matrix of the vertex transmissions in G and D(G) is the distance matrix of G. The largest eigenvalue of the distance signless Laplacian matrix is called the distance signless Laplacian spectral radius of G. In this paper, we determine the unique graph with the maximum distance signless Laplacian spectral radius among all the bicyclic graphs with given order.

关键词： distance signless Laplacian matrix spectral radius bicyclic graph

Unicyclic Graphs of Minimal spectral radius

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Acta Mathematica Sinica,English Series 2013年第2期29卷 281-286页

作者： Ling Sheng SHI Department of Mathematical Sciences Tsinghua University

It was conjectured by Li and Feng in 1979 that the unicyclic graph formed by a cycle of order g linking to an endvertex of a path of length k minimizes the spectral radius of all unicyclic graphs of order g ＋ k and girth g. In 1987, Cao proved that this conjecture is true for k ≥ g（g - 2）/8 and false for k = 2 and sufficiently large g. In this note, we show that g 〉12 suffices for the counterexample and give more counterexamples with large girth for any integer k 〉 1.

关键词： Extremal graph Li-Feng＇s conjecture spectral radius unicyclic

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lk,s-Singular values and spectral radius of partially symmetric rectangular tensors

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Frontiers of Mathematics in China 2016年第3期11卷 605-622页

作者： Hongmei YAO Bingsong LONG Changjiang BU Jiang ZHOU College of Science Harbin Engineering University Harbin 150001 China

The real rectangular tensors arise from the strong ellipticity condition problem in solid mechanics and the entanglement problem in quantum physics. In this paper, we first study properties oflk,singular values of real rectangular tensors. Then, a necessary and sufficient condition for the positive definiteness of partially symmetric rectangular tensors is given. Furthermore, we show that the weak Perron-Frobenius theorem for nonnegative partially symmetric rectangular tensor keeps valid under some new conditions and we prove a maximum property for the largest lk,S-singular values of nonnegative partially symmetric rectangular tensor. Finally, we prove that the largest lk,s- singular value of nonnegative weakly irreducible partially symmetric rectangular tensor is still geometrically simple.

关键词： lk,s-Singular values spectral radius positive definiteness partiallysymmetric rectangular tensor weakly irreducible

Hypergraphs with spectral radius at Most ■

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Journal of Mathematical Research with Applications 2019年第2期39卷 111-131页

作者： Shoudong MAN Linyuan LU Department of Mathematics Tianjin University of Finance and Economics Department of Mathematics University of South Carolina

In this paper, we consider the r-uniform hypergraphs H with spectral radius at most ■. We show that H must have a quipus-structure, which is similar to the graphs with spectral radius at most ■ [Woo-Neumaier, Graphs... 详细信息

关键词： r-uniform hypergraphs spectral radius α-normal

Estimations for the spectral radius of Nonnegative Tensors

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Journal of Mathematical Research with Applications 2020年第5期40卷 487-492页

作者： Aiquan JIAO School of Mathematical and Physical Science and Engineering Hebei University of Engineering

In this paper, a lower bound and an upper bound for the spectral radius of nonnegative tensors are obtained. Our new bounds are tighter than the corresponding bounds obtained by Li et al.(J. Inequal. Appl. 2015). A nu... 详细信息

关键词： bounds spectral radius nonnegative tensor irreducible

spectral radius of Non-negative Matrices and Digraphs

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Acta Mathematica Sinica,English Series 2002年第2期18卷 293-300页

作者： ZHANG Xiao Dong Department of Mathematics.East China Normal University,Shanghai 200062.P.R.China E-mail:xdzhang2@hotmail.comLI Jiong Sheng Department of Mathematics.University of Science and Technology of China,Hefei 230026,P.R China Department of Mathematics East China Normal University Shanghai P. R. China Department of Mathematics University of Science and Technology of China Hefei P. R. China

We present,an upper and a lower bound for the spectral radius of non-negative matrices. Then we give the bounds for the spectral radius of digraphs.

关键词： Non-negative matrix Digraph spectral radius

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Hypergraphs with spectral radius between Two Limit Points

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Journal of Mathematical Research with Applications 2018年第1期38卷 1-22页

作者： Shoudong MAN Linyuan LU Shuhua ZHANG Department of Mathematics Tianjin University of Finance and Economics Department of Mathematics University of South Carolina

In this paper, we set ρ;=;4;and ρ′;= β;, where β =-1/6 ·(100 + 12·（69）;);-2/(3·(100+12·（69）;));+4/3≈0.2451223338. We consider connected r-uniform hypergraphs with spectral radius between ρ;and ρ′;and ... 详细信息

关键词： r-uniform hypergraphs spectral radius α-normal