On the signless Laplacian Estrada index of uniform hypergraphs

2020 ◽  
Author(s):  
Hongyan Lu ◽  
Nini Xue ◽  
Zhongxun Zhu
Keyword(s):  
Estrada Index ◽  
Uniform Hypergraphs ◽  
Signless Laplacian

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.

scholarly journals Sharp bounds for ordinary and signless Laplacian spectral radii of uniform hypergraphs

2016 ◽  
Vol 285 ◽  
pp. 217-227 ◽  
Author(s):  
Hongying Lin ◽  
Biao Mo ◽  
Bo Zhou ◽  
Weiming Weng
Keyword(s):  
Sharp Bounds ◽  
Uniform Hypergraphs ◽  
Signless Laplacian

scholarly journals Graphs with maximum Laplacian and signless Laplacian Estrada index

2016 ◽  
Vol 339 (11) ◽  
pp. 2664-2671 ◽  
Author(s):  
Ivan Gutman ◽  
Luis Medina C ◽  
Pamela Pizarro ◽  
María Robbiano
Keyword(s):  
Estrada Index ◽  
Signless Laplacian

scholarly journals Sharp Lower Bounds on the Spectral Radius of Uniform Hypergraphs Concerning Degrees

10.37236/6644 ◽  
2018 ◽  
Vol 25 (2) ◽  
Author(s):  
Liying Kang ◽  
Lele Liu ◽  
Erfang Shan
Keyword(s):  
Lower Bound ◽  
Spectral Radius ◽  
Linear Algebra ◽  
Lower Bounds ◽  
Uniform Hypergraph ◽  
Uniform Hypergraphs ◽  
Signless Laplacian Tensor ◽  
Signless Laplacian ◽  
Vertex Degrees

Let $\mathcal{A}(H)$ and $\mathcal{Q}(H)$ be the adjacency tensor and signless Laplacian tensor of an $r$-uniform hypergraph $H$. Denote by $\rho(H)$ and $\rho(\mathcal{Q}(H))$ the spectral radii of $\mathcal{A}(H)$ and $\mathcal{Q}(H)$, respectively. In this paper we present a  lower bound on $\rho(H)$ in terms of vertex degrees and we characterize the extremal hypergraphs attaining the bound, which solves a problem posed by Nikiforov [Analytic methods for uniform hypergraphs, Linear Algebra Appl. 457 (2014) 455–535]. Also, we prove a lower bound on $\rho(\mathcal{Q}(H))$ concerning degrees and give a characterization of the extremal hypergraphs attaining the bound.

scholarly journals On maximum signless Laplacian Estrada index of graphs with given parameters

2016 ◽  
Vol 11 (2) ◽  
pp. 381-389 ◽  
Author(s):  
Hamid Reza Ellahi ◽  
Gholam Hossein Fath-Tabar ◽  
Ahmad Gholami ◽  
Ramin Nasiri
Keyword(s):  
Estrada Index ◽  
Signless Laplacian

scholarly journals On maximum signless Laplacian Estrada index of graphs with given parameters II

2018 ◽  
Vol 6 (1) ◽  
pp. 190 ◽  
Author(s):  
Ramin Nasiri ◽  
Hamid Reza Ellahi ◽  
Gholam Hossein Fath-Tabar ◽  
Ahmad Gholami
Keyword(s):  
Estrada Index ◽  
Signless Laplacian

scholarly journals Sharp bounds on the signless Laplacian Estrada index of graphs

Filomat ◽  
2014 ◽  
Vol 28 (10) ◽  
pp. 1983-1988 ◽  
Author(s):  
Shan Gao ◽  
Huiqing Liu
Keyword(s):  
Lower Bounds ◽  
Connected Graph ◽  
Laplacian Matrix ◽  
First Zagreb Index ◽  
Zagreb Index ◽  
Sharp Bounds ◽  
Estrada Index ◽  
Signless Laplacian Matrix ◽  
Signless Laplacian ◽  
The First Zagreb Index

Let G be a connected graph with n vertices and m edges. Let q1, q2,..., qn be the eigenvalues of the signless Laplacian matrix of G, where q1 ? q2 ? ... ? qn. The signless Laplacian Estrada index of G is defined as SLEE(G) = nPi=1 eqi. In this paper, we present some sharp lower bounds for SLEE(G) in terms of the k-degree and the first Zagreb index, respectively.

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