Eigenvalues of the adjacency tensor on products of hypergraphs

The cyclic index of adjacency tensor of generalized power hypergraphs

Discrete Mathematics ◽

10.1016/j.disc.2021.112329 ◽

2021 ◽

Vol 344 (5) ◽

pp. 112329

Author(s):

Yi-Zheng Fan ◽

Min Li ◽

Yi Wang

Keyword(s):

Adjacency Tensor

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Finding all H-Eigenvalues of Signless Laplacian Tensor for a Uniform Loose Path of Length Three

Asia Pacific Journal of Operational Research ◽

10.1142/s0217595920400072 ◽

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.

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Spectral Extremal Results for Hypergraphs

The Electronic Journal of Combinatorics ◽

10.37236/9018 ◽

2021 ◽

Vol 28 (3) ◽

Author(s):

Yuan Hou ◽

An Chang ◽

Joshua Cooper

Keyword(s):

Structural Properties ◽

Spectral Radius ◽

Spectral Methods ◽

Adjacency Tensor ◽

Uniform Hypergraphs ◽

Linear Hypergraph

Let $F$ be a graph. A hypergraph is called Berge $F$ if it can be obtained by replacing each edge in $F$ by a hyperedge containing it. Given a family of graphs $\mathcal{F}$, we say that a hypergraph $H$ is Berge $\mathcal{F}$-free if for every $F \in \mathcal{F}$, the hypergraph $H$ does not contain a Berge $F$ as a subhypergraph. In this paper we investigate the connections between spectral radius of the adjacency tensor and structural properties of a linear hypergraph. In particular, we obtain a spectral version of Turán-type problems over linear $k$-uniform hypergraphs by using spectral methods, including a tight result on Berge $C_4$-free linear $3$-uniform hypergraphs.

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Sub-hypergraph matching based on adjacency tensor

Computer Vision and Image Understanding ◽

10.1016/j.cviu.2019.03.003 ◽

2019 ◽

Vol 183 ◽

pp. 1-10 ◽

Cited By ~ 1

Author(s):

Jing Yang ◽

Xu Yang ◽

Zhang-Bing Zhou ◽

Zhi-Yong Liu

Keyword(s):

Adjacency Tensor ◽

Hypergraph Matching

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On Spectral Hypergraph Theory of the Adjacency Tensor

Graphs and Combinatorics ◽

10.1007/s00373-013-1340-x ◽

2013 ◽

Vol 30 (5) ◽

pp. 1233-1248 ◽

Cited By ~ 70

Author(s):

Kelly J. Pearson ◽

Tan Zhang

Keyword(s):

Adjacency Tensor ◽

Hypergraph Theory

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Minimal Non-Odd-Transversal Hypergraphs and Minimal Non-Odd-Bipartite Hypergraphs

The Electronic Journal of Combinatorics ◽

10.37236/9519 ◽

2020 ◽

Vol 27 (4) ◽

Author(s):

Yi-Zheng Fan ◽

Yi Wang ◽

Jiang-Chao Wan

Keyword(s):

Incidence Matrix ◽

Upper Bounds ◽

Simple Graphs ◽

Adjacency Tensor ◽

Uniform Hypergraphs ◽

Equivalent Characterization ◽

Vertex Set

Among all uniform hypergraphs with even uniformity, the odd-transversal or odd-bipartite hypergraphs are closer to bipartite simple graphs than bipartite hypergraphs from the viewpoint of both structure and spectrum. A hypergraph is called odd-transversal if it contains a subset of the vertex set such that each edge intersects the subset in an odd number of vertices, and it is called minimal non-odd-transversal if it is not odd-transversal but deleting any edge results in an odd-transversal hypergraph. In this paper we give an equivalent characterization of the minimal non-odd-transversal hypergraphs by means of the degrees and the rank of its incidence matrix over $\mathbb{Z}_2$. If a minimal non-odd-transversal hypergraph is uniform, then it has even uniformity, and hence is minimal non-odd-bipartite. We characterize $2$-regular uniform minimal non-odd-bipartite hypergraphs, and give some examples of $d$-regular uniform hypergraphs which are minimal non-odd-bipartite. Finally we give upper bounds for the least H-eigenvalue of the adjacency tensor of minimal non-odd-bipartite hypergraphs.

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