Author
Wenzhe Wang
Bio: Wenzhe Wang is an academic researcher from Harbin Engineering University. The author has contributed to research in topics: Sign (mathematics) & Rank (linear algebra). The author has an hindex of 6, co-authored 13 publications receiving 252 citations.
Papers
More filters
Posted Content•
TL;DR: Some spectral characterizations of odd-bipartite hypergraphs are given, and a partial answer to a question posed by Shao et al (2014) is given.
Abstract: For a $k$-uniform hypergraph $H$, we obtain some trace formulas for the Laplacian tensor of $H$, which imply that $\sum_{i=1}^nd_i^s$ ($s=1,\ldots,k$) is determined by the Laplacian spectrum of $H$, where $d_1,\ldots,d_n$ is the degree sequence of $H$. Using trace formulas for the Laplacian tensor, we obtain expressions for some coefficients of the Laplacian polynomial of a regular hypergraph. We give some spectral characterizations of odd-bipartite hypergraphs, and give a partial answer to a question posed by Shao et al \cite{ShaoShanWu}. We also give some spectral properties of power hypergraphs, and show that a conjecture posed by Hu et al \cite{HuQiShao} holds under certain conditons.
69 citations
TL;DR: In this article, the Laplacian tensor tensor of a regular hypergraph is derived from the spectrum of the degree sequence of the hypergraph, and the spectral properties of power hypergraphs are studied.
Abstract: For a $k$-uniform hypergraph $H$, we obtain some trace formulas for the Laplacian tensor of $H$, which imply that $\sum_{i=1}^nd_i^s$ ($s=1,\ldots,k$) is determined by the Laplacian spectrum of $H$, where $d_1,\ldots,d_n$ is the degree sequence of $H$. Using trace formulas for the Laplacian tensor, we obtain expressions for some coefficients of the Laplacian polynomial of a regular hypergraph. We give some spectral characterizations of odd-bipartite hypergraphs, and give a partial answer to a question posed by Shao et al (2014). We also give some spectral properties of power hypergraphs, and show that a conjecture posed by Hu et al (2013) holds under certain conditons.
62 citations
TL;DR: In this paper, an application of resistance distances to the bipartiteness of graphs is given, and an interlacing inequality for eigenvalues of the resistance matrix and the Laplacian matrix is given.
Abstract: In this paper, we obtain formulas for resistance distances and Kirchhoff index of subdivision graphs. An application of resistance distances to the bipartiteness of graphs is given. We also give an interlacing inequality for eigenvalues of the resistance matrix and the Laplacian matrix.
59 citations
TL;DR: In this paper, the rank of a uniform hypergraph is independent of the ordering of its vertices and the Laplacian tensor has the same rank for odd-bipartite even-uniform hypergraphs.
55 citations
TL;DR: This paper proves that Cn ○ 2K1 is determined by its signless Laplacian spectrum when n ≠ 32, 64.
Abstract: For a cycle C n , let C n ? 2K 1 be the graph obtained from C n by attaching two pendant edges to each vertex of C n . In this paper, we prove that C n ? 2K 1 is determined by its signless Laplacian spectrum when n ? 32, 64. We also show that C n ? 2K 1 is determined by its Laplacian spectrum.
15 citations
Cited by
More filters
01 Jan 2009
TL;DR: In this article, the authors introduce the concept of graph operations and modifications, and characterizations of spectra by characterizations by spectra and one eigenvalue, and Laplacians.
Abstract: Preface 1. Introduction 2. Graph operations and modifications 3. Spectrum and structure 4. Characterizations by spectra 5. Structure and one eigenvalue 6. Spectral techniques 7. Laplacians 8. Additional topics 9. Applications Appendix Bibliography Index of symbols Index.
398 citations
[...]
TL;DR: In this paper, the adjacency matrix, a matrix of O's and l's, is used to store a graph or digraph in a computer, and certain matrix operations are seen to correspond to digraph concepts.
Abstract: In order to store a graph or digraph in a computer, we need something other than the diagram or the formal definition. This something is the adjacency matrix, a matrix of O’s and l’s. The l’s correspond to the arcs of the digraph. Certain matrix operations will be seen to correspond to digraph concepts.
292 citations
01 Jan 2016
TL;DR: An introduction to the theory of graph spectra is available in the book collection an online access to it is set as public so you can download it instantly and is universally compatible with any devices to read.
Abstract: an introduction to the theory of graph spectra is available in our book collection an online access to it is set as public so you can download it instantly. Our digital library hosts in multiple countries, allowing you to get the most less latency time to download any of our books like this one. Merely said, the an introduction to the theory of graph spectra is universally compatible with any devices to read.
222 citations
TL;DR: It is proved that a nonsingular $$\mathcal {M}$$M-equations with a positive right-hand side always has a unique positive solution.
Abstract: This paper is concerned with solving some structured multi-linear systems, especially focusing on the equations whose coefficient tensors are $$\mathcal {M}$$M-tensors, or called $$\mathcal {M}$$M-equations for short. We prove that a nonsingular $$\mathcal {M}$$M-equation with a positive right-hand side always has a unique positive solution. Several iterative algorithms are proposed for solving multi-linear nonsingular $$\mathcal {M}$$M-equations, generalizing the classical iterative methods and the Newton method for linear systems. Furthermore, we apply the $$\mathcal {M}$$M-equations to some nonlinear differential equations and the inverse iteration for spectral radii of nonnegative tensors.
156 citations