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Computing the p-Spectral Radii of Uniform Hypergraphs with Applications
[article]

2017
*
arXiv
*
pre-print

When

arXiv:1703.04275v1
fatcat:a6q5fppaljdelau2mrsj7i62qe
*computing**the**spectral*radius*of**the*adjacency tensor*of*a*uniform**hypergraph*, CSRH stands out among existing approaches. ...*The**p*-*spectral*radius*of*a*uniform**hypergraph*covers many important concepts, such as Lagrangian and*spectral*radius*of**the**hypergraph*, and is crucial for solving*spectral*extremal problems*of**hypergraphs*... In this paper, we focus on*the**computation**of**p*-*spectral**radii**of**uniform**hypergraphs*.*The**p*-*spectral*radius*of*a*hypergraph*was introduced in [32] and linked*with*extremal*hypergraph*problems. ...##
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On some properties of the α-spectral radius of the k-uniform hypergraph
[article]

2019
*
arXiv
*
pre-print

We characterize

arXiv:1905.07691v1
fatcat:dinzsyzjazgwhlgtjetepc7aqi
*the*extremal hypertree for α-*spectral*radius among k-*uniform*non-caterpillar*hypergraphs**with*given order, size and diameter. we also characerize*the*second largest α-*spectral*radius among ... In this paper we show how*the*α-*spectral*radius changes under*the*edge grafting operations on connected k-*uniform**hypergraphs*. ... Lu,*The*maximum*spectral**radii**of**uniform*supertrees*with*given degree sequences, Linear Algebra and its*Applications*523 (2017) 33–45. [17] S. Hu, L. Qi, J.-Y. ...##
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The α-normal labeling method for computing the p-spectral radii of uniform hypergraphs
[article]

2018
*
arXiv
*
pre-print

In this paper, we extend Lu and Man's α-normal labeling method to

arXiv:1803.06385v1
fatcat:zjbcpwjbsjhvfk7gm5bz2wqzyy
*the**p*-*spectral**radii**of**uniform**hypergraphs*for*p*r; and find some*applications*. ...*The*α-normal labeling method, which was introduced by Lu and Man in 2014, is effective method for*computing**the**spectral**radii**of**uniform**hypergraphs*. ... In [10] , Lu and Man introduced*the*α-normal labeling method for*computing**the**spectral**radii**of**uniform**hypergraphs*as follows: Theorem 1.1 ( [10] ) Let G be a connected r-*uniform**hypergraph*. ...##
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The extremal spectral radii of k-uniform supertrees
[article]

2014
*
arXiv
*
pre-print

We also determine

arXiv:1405.7257v1
fatcat:fik3ilgronbbxhvw3mbjea635y
*the*unique k-*uniform*supertree on n vertices*with**the*second largest*spectral*radius (for these three kinds*of**spectral**radii*). ... In this paper, we study some extremal problems*of*three kinds*of**spectral**radii**of*k-*uniform**hypergraphs*(*the*adjacency*spectral*radius,*the*signless Laplacian*spectral*radius and*the*incidence Q-*spectral*... some upper and lower bounds*of**the*incidence Q-*spectral**radii**of**uniform**hypergraphs*. ...##
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The extremal spectral radii of $$k$$ k -uniform supertrees

2015
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Journal of combinatorial optimization
*

We also determine

doi:10.1007/s10878-015-9896-4
fatcat:nyxzfqqlevdedptmdk3zkjcogm
*the*unique k-*uniform*supertree on n vertices*with**the*second largest*spectral*radius (for these three kinds*of**spectral**radii*). ... Abstract In this paper, we study some extremal problems*of*three kinds*of**spectral**radii**of*k-*uniform**hypergraphs*(*the*adjacency*spectral*radius,*the*signless Laplacian*spectral*radius and*the*incidence ... As*applications*, we determine*the*unique k-*uniform*supertrees on n vertices*with**the*largest and second largest*spectral**radii*, and determine*the*unique k-*uniform*hypertree on n vertices*with**the*smallest ...##
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The matching polynomials and spectral radii of uniform supertrees
[article]

2018
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arXiv
*
pre-print

We study matching polynomials

arXiv:1807.01180v1
fatcat:elbnrsdttjgrtnr6mogvwo2xsq
*of**uniform**hypergraph*and*spectral**radii**of**uniform*supertrees. ... In addition,*the*first two smallest*spectral**radii**of*supertrees*with*size m are determined. ... Recently,*the*first two largest*spectral**radii**of**uniform*supertrees*with*given diameter were characterized in [28] . ...##
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Connected hypergraphs with small spectral radius

2016
*
Linear Algebra and its Applications
*

We discovered a novel method for

doi:10.1016/j.laa.2016.07.013
fatcat:tpenelmew5fxjiwd3yurvhjy24
*computing**the**spectral*radius*of**hypergraphs*, and classified all connected r-*uniform**hypergraphs**with**spectral*radius at most ρr. ... We show that*the*smallest limit point*of**the**spectral**radii**of*connected r-*uniform**hypergraphs*is ρr = r √ 4. ... For any*p*≥ 1,*the*largest*p*-eigenvalue*of*H is defined as λ*p*(H) = max x*p*=1*P*H (x). In this paper, we define*the**spectral*radius*of*an r-*uniform**hypergraph*H to be ρ(H) = λ r (H). ...##
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The Matching Polynomials and Spectral Radii of Uniform Supertrees

2018
*
Electronic Journal of Combinatorics
*

We study matching polynomials

doi:10.37236/7839
fatcat:zrsnt2ogqrgmve2tmxujyy3lem
*of**uniform**hypergraph*and*spectral**radii**of**uniform*supertrees. ... In addition,*the*first two smallest*spectral**radii**of*supertrees*with*size $m$ are determined. ... In this paper, we determine*the*first d 2 + 1 largest*spectral**radii**of*supertrees among all r-*uniform*supertrees*with*size m and diameter d and*the*first two smallest*spectral**radii**of*supertrees*with*...##
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A Bound on the Spectral Radius of Hypergraphs with e Edges
[article]

2017
*
arXiv
*
pre-print

We prove that

arXiv:1705.01593v1
fatcat:t5dwhdwh7fdfvmtwmkrjxnnrx4
*the**spectral*radius*of*an r-*uniform**hypergraph*H*with*e edges is at most f_r(e). ...*The*equality holds if and only if e=k r for some positive integer k and H is*the*union*of*a complete r-*uniform**hypergraph*K_k^r and some possible isolated vertices. ... determined*the*extremal*spectral**radii**of*several classes*of*r-*uniform**hypergraphs**with*few edges. ...##
###
Page 4393 of Mathematical Reviews Vol. , Issue 81K
[page]

1981
*
Mathematical Reviews
*

Also

*the*class*of*complete n-partite graphs*with**p*points may be ordered by*the**spectral**radii**of**the*graphs (two such graphs*with**the*same spec- tral radius are isomorphic). ... A*p*-graph is a*uniform**hypergraph*(each edge*of*which has*the*same cardinality*p*). A*p*-graph*with*n vertices and r edges is said to be*of*degree pr/n. ...##
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The Spectral Radii of Intersecting Uniform Hypergraphs

2020
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Communications on Applied Mathematics and Computation
*

This paper states

doi:10.1007/s42967-020-00073-7
fatcat:qizeyvoywvazpm7wzvrgqlflva
*spectral*versions*of**the*Erdős-Ko-Rado theorem: let G be an intersecting k-*uniform**hypergraph*on n vertices*with*n ⩾ 2k. ... Then,*the*sharp upper bounds for*the**spectral*radius*of*A (G) and is a convex linear combination*of**the*degree diagonal tensor D(G) and*the*adjacency tensor A(G) for 0 ⩽ < 1, and Q * (G) is*the*incidence ... improvement*of**the*presentation. ...##
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The smallest spectral radius of bicyclic uniform hypergraphs with a given size
[article]

2020
*
arXiv
*
pre-print

In this paper, we study

arXiv:2010.01525v1
fatcat:ioyjploywncrljhwkiqs7hgiau
*the*log-concavity*of*a type*of*iteration sequence related to*the*α-normal weighted incidence matrices which is presented by Lu and Man for*computing**the**spectral*radius*of**hypergraphs*... By using results obtained about*the*sequence and*the*method*of*some edge operations, we will characterize completely extremal k-graphs*with**the*smallest*spectral*radius among bicyclic*hypergraphs**with*... Recently, Zhang et al. determine*the**uniform**hypergraphs**of*size m*with**the*first two smallest*spectral**radii*[8] . ...##
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The first few unicyclic and bicyclic hypergraphs with larger spectral radii
[article]

2016
*
arXiv
*
pre-print

In this paper we investigate

arXiv:1607.08291v1
fatcat:xog5pl7y4bbkhgm443fn2f6dnu
*hypergraphs*that attain larger*spectral**radii*among all simple connected k-*uniform*unicyclic and bicyclic*hypergraphs*. ...*with*larger*spectral*radius among all unicyclic*hypergraphs*and*the*first three over all bicyclic*hypergraphs*. ... In Section 3,*with**the**application**of*all these tools,*the*first five*hypergraphs**with*larger*spectral**radii*among all unicyclic k-graphs are determined. ...##
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A sharp upper bound on the spectral radius of a nonnegative k-uniform tensor and its applications to (directed) hypergraphs

2020
*
Journal of Inequalities and Applications
*

Zhang,

doi:10.1186/s13660-020-2305-2
fatcat:nfimsx3gmjcjlaqqzbcdywvhbm
*Spectral*radius*of**uniform**hypergraphs*and degree sequences, Front. Math. ... China 6:1279-1288, 2017]; and presents some new sharp upper bounds for*the*adjacency*spectral*radius and signless Laplacian*spectral*radius*of*a*uniform*directed*hypergraph*. ... Acknowledgements*The*authors would like to thank*the*referees for their valuable comments, corrections, and suggestions, which lead to an improvement*of**the*original manuscript. ...##
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Nonbacktracking spectral clustering of nonuniform hypergraphs
[article]

2022
*
arXiv
*
pre-print

We study

arXiv:2204.13586v1
fatcat:3zklyu7o2fdtnnzkpewttkyxmy
*spectral*clustering for nonuniform*hypergraphs*based on*the**hypergraph*nonbacktracking operator. ... Through an analysis*of*our algorithm, we pose several conjectures about*the*limits*of**spectral*methods and detectability in*hypergraph*stochastic blockmodels writ large. ...*The*nonbacktracking matrix B has found several*applications*in*the**the*study*of*graphs (i.e., 2-*uniform**hypergraphs*). Alon et al. ...
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