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

Jingya Chang, Weiyang Ding, Liqun Qi, Hong Yan
2017 arXiv   pre-print
When 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.  ... 
arXiv:1703.04275v1 fatcat:a6q5fppaljdelau2mrsj7i62qe

On some properties of the α-spectral radius of the k-uniform hypergraph [article]

Feifei Wang, Haiying Shan, Zhiyi Wang
2019 arXiv   pre-print
We characterize 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.  ... 
arXiv:1905.07691v1 fatcat:dinzsyzjazgwhlgtjetepc7aqi

The α-normal labeling method for computing the p-spectral radii of uniform hypergraphs [article]

Lele Liu, Linyuan Lu
2018 arXiv   pre-print
In this paper, we extend Lu and Man's α-normal labeling method to 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.  ... 
arXiv:1803.06385v1 fatcat:zjbcpwjbsjhvfk7gm5bz2wqzyy

The extremal spectral radii of k-uniform supertrees [article]

Honghai Li, Jiayu Shao, Liqun Qi
2014 arXiv   pre-print
We also determine 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.  ... 
arXiv:1405.7257v1 fatcat:fik3ilgronbbxhvw3mbjea635y

The extremal spectral radii of $$k$$ k -uniform supertrees

Honghai Li, Jia-Yu Shao, Liqun Qi
2015 Journal of combinatorial optimization  
We also determine 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  ... 
doi:10.1007/s10878-015-9896-4 fatcat:nyxzfqqlevdedptmdk3zkjcogm

The matching polynomials and spectral radii of uniform supertrees [article]

Li Su, Liying Kang, Honghai Li, Erfang Shan
2018 arXiv   pre-print
We study matching polynomials 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] .  ... 
arXiv:1807.01180v1 fatcat:elbnrsdttjgrtnr6mogvwo2xsq

Connected hypergraphs with small spectral radius

Linyuan Lu, Shoudong Man
2016 Linear Algebra and its Applications  
We discovered a novel method for 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).  ... 
doi:10.1016/j.laa.2016.07.013 fatcat:tpenelmew5fxjiwd3yurvhjy24

The Matching Polynomials and Spectral Radii of Uniform Supertrees

Li Su, Liying Kang, Honghai Li, Erfang Shan
2018 Electronic Journal of Combinatorics  
We study matching polynomials 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  ... 
doi:10.37236/7839 fatcat:zrsnt2ogqrgmve2tmxujyy3lem

A Bound on the Spectral Radius of Hypergraphs with e Edges [article]

Shuliang Bai, Linyuan Lu
2017 arXiv   pre-print
We prove that 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.  ... 
arXiv:1705.01593v1 fatcat:t5dwhdwh7fdfvmtwmkrjxnnrx4

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.  ... 

The Spectral Radii of Intersecting Uniform Hypergraphs

Peng-Li Zhang, Xiao-Dong Zhang
2020 Communications on Applied Mathematics and Computation  
This paper states 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.  ... 
doi:10.1007/s42967-020-00073-7 fatcat:qizeyvoywvazpm7wzvrgqlflva

The smallest spectral radius of bicyclic uniform hypergraphs with a given size [article]

Haiying Shan, Zhiyi Wang, Feifei Wang
2020 arXiv   pre-print
In this paper, we study 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] .  ... 
arXiv:2010.01525v1 fatcat:ioyjploywncrljhwkiqs7hgiau

The first few unicyclic and bicyclic hypergraphs with larger spectral radii [article]

Chen Ouyang, Liqun Qi, Xiying Yuan
2016 arXiv   pre-print
In this paper we investigate 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.  ... 
arXiv:1607.08291v1 fatcat:xog5pl7y4bbkhgm443fn2f6dnu

A sharp upper bound on the spectral radius of a nonnegative k-uniform tensor and its applications to (directed) hypergraphs

Chuang Lv, Lihua You, Xiao-Dong Zhang
2020 Journal of Inequalities and Applications  
Zhang, 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.  ... 
doi:10.1186/s13660-020-2305-2 fatcat:nfimsx3gmjcjlaqqzbcdywvhbm

Nonbacktracking spectral clustering of nonuniform hypergraphs [article]

Philip Chodrow, Nicole Eikmeier, Jamie Haddock
2022 arXiv   pre-print
We study 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.  ... 
arXiv:2204.13586v1 fatcat:3zklyu7o2fdtnnzkpewttkyxmy
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