2021年图谱与超图的张量谱理论研讨会

2021年图谱与超图的张量谱理论研讨会

1会议时间：2021424日，

2报告安排：邀请每位参会老师做报告，报告时间为40分钟，

3腾讯会议ID693 826 297

刘乐乐：ahhylau@163.com

吴宝丰：baufern@aliyun.com

邵嘉裕：jyshao@tongji.edu.cn

 时间 报告人及题目 主持人 09:00   – 09:10 邵嘉裕教授致辞 何常香 09:10 – 09:50 报告人: 黄琼湘题目: The extremal graphs of order trees and their topological indices 王维凡 09:50 – 10:30 报告人: 张胜贵题目: 代数连通度在多智能体系统一致性研究中的应用 王维凡 10:30 – 11: 10 报告人: 侯耀平题目: Eigenvalue multiplicity in cubic signed graphs 卜长江 11:10 – 11:50 报告人: 冯立华题目: On the extensional eigenvalues of graphs 卜长江 14:00 – 14:40 报告人: 晏卫根题目: Solution of the monomer-dimer model on a fractal scale-free lattice 范益政 14:40 – 15:20 报告人: 翟明清题目: Spectral extrema of graphs with given size 范益政 15:20 – 16:00 报告人: 刘慧清题目: On the skew spectral moments of graphs 常安 16:00 – 16: 40 报告人: 李红海题目: Polynomials and spectral radius of hypergraphs 常安 16:40 – 17: 20 报告人: 刘乐乐题目: The $\alpha$-normal labeling method for computing the p-spectral radii   of uniform hypergraphs 何常香

The extremal graphs of order trees and their topological indices

Eigenvalue multiplicity in cubic signed graphs

On the extensional eigenvalues of graphs

Solution of the monomer-dimer model on a fractal scale-free lattice

This is joint work with Danyi Li and Shuli Li.

Spectral extrema of graphs with given size

If the first parameter is n(G) and the second is m(G), then we get the classic Turan problem. Nikiforov posed a spectral analog by replacing m(G) with \rho(G) in the classic Turan problem. In the past decade, much attention has been paid to this spectra Turan-type problem. In this talk, we survey some classic spectral bounds on graphs with given size. Along this line, we introduce a new version of spectral Turan-type problem.

This is a joint work with Huiqiu Lin and Jinlong Shu.

On the skew spectral moments of graphs

Let G be a simple graph, and $G^{\sigma}$ be an oriented graph of G with the orientation $\sigma$ and skew-adjacency matrix $S(G^{\sigma})$. Let $\lambda_1(G^{\sigma})$,$\lambda_2(G^{\sigma})$,$\ldots$,$\lambda_n(G^{\sigma})$ be the eigenvalues of $S(G^{\sigma})$. The number $\sum_{i=1}^n \lambda_i^k(G^{\sigma})$ (k=0,1,,n-1), is called the k-th skew spectral moment of $G^{\sigma}$, denoted by $T_k(G^{\sigma})$, and $T(G^{\sigma}) = (T_0(G^{\sigma}), T_1(G^{\sigma}),,T_{n1}(G^{\sigma}))$ is the sequence of

skew spectral moments of $G^{\sigma}$. Suppose $G_1^{\sigma_1}$ and $G_2^{\sigma_2}$ are two digraphs. We shall write $G_1^{\sigma_1} \prec G_2^{\sigma_2}$ if for some k ($1 \leq k \leq n1$), $T_i(G_1^{\sigma_1}) = T_i(G_2^{\sigma_2})$ ($i = 0,1,,k1$) and $T_k (G_1^{\sigma_1})< T_k (G_2^{\sigma_2})$ hold. In this talk, we will present some results on the T-order of oriented trees with diameter d and unicyclic graphs with girth g.

Polynomials and spectral radius of hypergraphs

We introduce matching polynomials of hypergraphs and then an ordering on hypertrees by positivity of the difference of matching polynomials. It is shown that the ordering of hypertrees is compatible with the order of their spectral radii in value. However, the determination of the ordering of hypertrees is usually easier than comparing their spectral radius directly. Using matching polynomial method, together with edge-moving theorem and so on, the first two largest hypertrees among all hypertrees with given size and strong stability number can be determined.

The $\alpha$-normal labeling method for computing the p-spectral

radii of uniform hypergraphs

$\lambda^{(p)}(G):=\max_{|x_1|^p+\cdots+|x_n|^p=1} r\sum_{\{i_1,\ldots,i_r\}\in E(G)}x_{i_1}\cdots x_{i_r}.$

The p-spectral radius was introduced by Keevash-Lenz-Mubayi, and subsequently studied by Nikiforov in 2014. The most extensively studied case is when p=r, and $\lambda^{(r)}(G)$ is called the spectral radius of G. The \alpha-normal labeling method, which was introduced by Lu and Man in 2014, is effective method for computing the spectral radii of uniform hypergraphs. It labels each corner of an edge by a positive number so that the sum of the corner labels at any vertex is 1 while the product of all corner labels at any edge is \alpha. Since then, this method has been used by many researchers in studying $\lambda^{(r)}(G)$. In this paper, we extend Lu and Man's \alpha-normal labeling method to the p-spectral radii of uniform hypergraphs for p\ne r; and find some applications.

This is a joint work with Linyuan Lu.

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