scholarly journals Spectral Extremal Results for Hypergraphs

10.37236/9018 ◽  
2021 ◽  
Vol 28 (3) ◽  
Author(s):  
Yuan Hou ◽  
An Chang ◽  
Joshua Cooper
Keyword(s):  
Structural Properties ◽  
Spectral Radius ◽  
Spectral Methods ◽  
Adjacency Tensor ◽  
Uniform Hypergraphs ◽  
Linear Hypergraph

Let $F$ be a graph. A hypergraph is called Berge $F$ if it can be obtained by replacing each edge in $F$ by a hyperedge containing it. Given a family of graphs $\mathcal{F}$, we say that a hypergraph $H$ is Berge $\mathcal{F}$-free if for every $F \in \mathcal{F}$, the hypergraph $H$ does not contain a Berge $F$ as a subhypergraph. In this paper we investigate the connections between spectral radius of the adjacency tensor and structural properties of a linear hypergraph. In particular, we obtain a spectral version of Turán-type problems over linear $k$-uniform hypergraphs by using spectral methods, including a tight result on Berge $C_4$-free linear $3$-uniform hypergraphs.

Finding all H-Eigenvalues of Signless Laplacian Tensor for a Uniform Loose Path of Length Three

2020 ◽  
Vol 37 (04) ◽  
pp. 2040007
Author(s):  
Junjie Yue ◽  
Liping Zhang
Keyword(s):  
Numerical Results ◽  
Geometric Structures ◽  
Special Formula ◽  
Adjacency Tensor ◽  
Uniform Hypergraphs ◽  
Signless Laplacian Tensor ◽  
Signless Laplacian

H-spectra of adjacency tensor, Laplacian tensor, and signless Laplacian tensor are important tools for revealing good geometric structures of the corresponding hypergraph. It is meaningful to compute H-spectra for some special [Formula: see text]-uniform hypergraphs. For an odd-uniform loose path of length three, the Laplacian H-spectrum has been studied. In this paper, we compute all signless Laplacian H-eigenvalues for the class of loose paths. We show that the number of H-spectrum of signless Laplacian tensor for an odd(even)-uniform loose path with length three is [Formula: see text]([Formula: see text]). Some numerical results are given to show the efficiency of our method. Especially, the numerical results show that the H-spectrum is convergent when [Formula: see text] goes to infinity. Finally, we present a conjecture that the signless Laplacian H-spectrum converges to [Formula: see text] ([Formula: see text]) for odd (even)-uniform loose path of length three.

Bounds on the spectral radius of uniform hypergraphs

2019 ◽  
Vol 259 ◽  
pp. 160-169 ◽  
Author(s):  
Lele Liu ◽  
Liying Kang ◽  
Shuliang Bai
Keyword(s):  
Spectral Radius ◽  
Uniform Hypergraphs

scholarly journals The p-spectral radius of k-partite and k-chromatic uniform hypergraphs

2015 ◽  
Vol 478 ◽  
pp. 81-107 ◽  
Author(s):  
L. Kang ◽  
V. Nikiforov ◽  
X. Yuan
Keyword(s):  
Spectral Radius ◽  
Uniform Hypergraphs

scholarly journals Distance spectral radius of uniform hypergraphs

2016 ◽  
Vol 506 ◽  
pp. 564-578 ◽  
Author(s):  
Hongying Lin ◽  
Bo Zhou
Keyword(s):  
Spectral Radius ◽  
Uniform Hypergraphs

On the spectral radii and principal eigenvectors of uniform hypergraphs

2017 ◽  
Vol 09 (04) ◽  
pp. 1750048 ◽  
Author(s):  
Xuelian Si ◽  
Xiying Yuan
Keyword(s):  
Spectral Radius ◽  
Lower Bounds ◽  
Uniform Hypergraph ◽  
Principal Eigenvector ◽  
Uniform Hypergraphs ◽  
Positive Eigenvector ◽  
Spectral Radius Formula

Let [Formula: see text] be a connected [Formula: see text]-uniform hypergraph. The unique positive eigenvector [Formula: see text] with [Formula: see text] corresponding to spectral radius [Formula: see text] is called the principal eigenvector of [Formula: see text]. In this paper, we present some lower bounds for the spectral radius [Formula: see text] and investigate the bounds of entries of the principal eigenvector of [Formula: see text].

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