The effect on the (signless Laplacian) spectral radii of uniform hypergraphs by subdividing an edge

2020 ◽  
Vol 283 ◽  
pp. 444-455 ◽  
Author(s):  
Peng Xiao ◽  
Ligong Wang
Keyword(s):  
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 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.

Upper bounds for signless Laplacian Z-spectral radius of uniform hypergraphs

2019 ◽  
Vol 14 (1) ◽  
pp. 17-24
Author(s):  
Jun He ◽  
Yanmin Liu ◽  
Junkang Tian ◽  
Xianghu Liu
Keyword(s):  
Spectral Radius ◽  
Upper Bounds ◽  
Uniform Hypergraphs ◽  
Signless Laplacian

scholarly journals The (signless Laplacian) spectral radius (of subgraphs) of uniform hypergraphs

Filomat ◽  
2019 ◽  
Vol 33 (15) ◽  
pp. 4733-4745 ◽  
Author(s):  
Cunxiang Duan ◽  
Ligong Wang ◽  
Peng Xiao ◽  
Xihe Li
Keyword(s):  
Spectral Radius ◽  
Lower Bounds ◽  
Maximum Degree ◽  
Uniform Hypergraph ◽  
Laplacian Spectral Radius ◽  
Signless Laplacian Spectral Radius ◽  
Uniform Hypergraphs ◽  
Signless Laplacian ◽  
Proper Subgraph

Let ?1(G) and q1(G) be the spectral radius and the signless Laplacian spectral radius of a kuniform hypergraph G, respectively. In this paper, we give the lower bounds of d-?1(H) and 2d-q1(H), where H is a proper subgraph of a f (-edge)-connected d-regular (linear) k-uniform hypergraph. Meanwhile, we also give the lower bounds of 2?-q1(G) and ?-?1(G), where G is a nonregular f (-edge)-connected (linear) k-uniform hypergraph with maximum degree ?.

scholarly journals Energies of Hypergraphs

2020 ◽  
Vol 36 (36) ◽  
pp. 293-308
Author(s):  
Kauê Cardoso ◽  
Vilmar Trevisan
Keyword(s):  
Spectral Radius ◽  
Maximum Degree ◽  
Zagreb Index ◽  
Uniform Hypergraphs ◽  
Subdivision Graph ◽  
Laplacian Energy ◽  
Signless Laplacian

In this paper, energies associated with hypergraphs are studied. More precisely, results are obtained for the incidence and the singless Laplacian energies of uniform hypergraphs. In particular, bounds for the incidence energy are obtained as functions of well known parameters, such as maximum degree, Zagreb index and spectral radius. It is also related the incidence and signless Laplacian energies of a hypergraph with the adjacency energies of its subdivision graph and line multigraph, respectively. In addition, the signless Laplacian energy for the class of the power hypergraphs is computed.

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