On the Z-eigenvalues of the signless Laplacian tensor for an even uniform hypergraph

2013 ◽  
Vol 20 (6) ◽  
pp. 1030-1045 ◽  
Author(s):  
Jinshan Xie ◽  
An Chang
Keyword(s):  
Uniform Hypergraph ◽  
Signless Laplacian Tensor ◽  
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.

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 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 The minimum covering signless laplacian energy of graph

2020 ◽  
Vol 1597 ◽  
pp. 012031
Author(s):  
Kavita Permi ◽  
H S Manasa ◽  
M C Geetha
Keyword(s):  
Laplacian Energy ◽  
Signless Laplacian ◽  
Energy Of Graph

scholarly journals On the Second-Largest Reciprocal Distance Signless Laplacian Eigenvalue

Mathematics ◽  
2021 ◽  
Vol 9 (5) ◽  
pp. 512
Author(s):  
Maryam Baghipur ◽  
Modjtaba Ghorbani ◽  
Hilal A. Ganie ◽  
Yilun Shang
Keyword(s):  
Lower Bounds ◽  
Complete Graph ◽  
Distance Matrix ◽  
Upper And Lower Bounds ◽  
Laplacian Eigenvalue ◽  
Signless Laplacian ◽  
Graph Parameters ◽  
Simple Connected Graph ◽  
Second Largest Eigenvalue ◽  
Reciprocal Distance Matrix

The signless Laplacian reciprocal distance matrix for a simple connected graph G is defined as RQ(G)=diag(RH(G))+RD(G). Here, RD(G) is the Harary matrix (also called reciprocal distance matrix) while diag(RH(G)) represents the diagonal matrix of the total reciprocal distance vertices. In the present work, some upper and lower bounds for the second-largest eigenvalue of the signless Laplacian reciprocal distance matrix of graphs in terms of various graph parameters are investigated. Besides, all graphs attaining these new bounds are characterized. Additionally, it is inferred that among all connected graphs with n vertices, the complete graph Kn and the graph Kn−e obtained from Kn by deleting an edge e have the maximum second-largest signless Laplacian reciprocal distance eigenvalue.

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