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

为了加强图谱与超图的张量谱理论的学术交流，促进同行之间学术研究水平的提升，上海理工大学和同济大学联合于2021年4月24日举办线上“图谱与超图的张量谱理论”研讨会。会议将围绕图谱和超图的张量谱等领域的问题，深入探讨谱理论的最新研究成果及其在各领域的应用。研讨会的主旨是研究成果交流、国内外研究动态介绍和评述等。

会议的具体事宜如下：

1、会议时间：2021年4月24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ID：693 826 297。

联系人：何常香：changxiang-he@163.com

  刘乐乐：ahhylau@163.com

  吴宝丰：baufern@aliyun.com

  邵嘉裕：jyshao@tongji.edu.cn

会议日程(2021/04/24)

题目与摘要

The extremal graphs of order trees and their topological indices

黄琼湘  新疆大学

摘要: Recently, D. Vukicevic and J. Sedlar in [D. Vukicevic, J. Sedlar, On indices of Wiener and anti-Wiener type, Discrete Appl. Math. 251 (2018) 290--298.] introduced an order ``$\preceq$ on T_n, the set of trees on n vertices, such that the topological index F of a graph is a function defined on the order set . It provides a new approach to determine the extremal graphs with respect to topological index F. By using the method they determined the common maximum and/or minimum graphs of T_n with respect to topological indices of Wiener type and anti-Wiener type. Motivated by their researches we further study the order set and give a criterion to determine its order, which enable us to get the common extremal graphs in four prescribed subclasses of . All these extremal graphs are confirmed to be the common maximum and/or minimum graphs with respect to the topological indices of Wiener type and anti-Wiener type. Additionally, we calculate the exact values of Wiener index for the extremal graphs in the order sets , and .

报告人简介:黄琼湘，新疆大学数学与系统科学学院教授，博士生导师。近年来主要从事代数图论，特别是图谱理论的研究。主持完成重点项目子项目 1 项，国家自然科学基金3项。在 J. Combin. Theory Ser. B，Europ. J. Combin.，Electronic Journal of Combinatorics，J. Algebraic Combin.，Discrete Math.， Discrete Appl. Math.，Linear Algebra Appl. 等主流学术期刊上发表论文 120 余篇。

代数连通度在多智能体系统一致性研究中的应用

张胜贵西北工业大学

摘要:本报告主要介绍图的代数连通度在多智能体系统一致性问题研究中的重要应用. 通信网络的代数连通度决定了一致性协议的收敛速度: 代数连通度越大, 一致性协议的收敛速度越快. 而且, 通信网络的代数连通度对多智能体系统的通信量、通信延迟上限等都有影响: 对有通信时延的一致性协议, 代数连通度越大, 系统可允许较大的通信时延; 对周期通信和事件触发的一致性协议, 代数连通度越大, 智能体间的通信频率可以更低, 系统达成一致需要的通信量更少. 同时, 本报告将总结优化代数连通度的各种方法, 并提出了若干待解决的问题.

报告人简介:张胜贵，荷兰Twente大学博士，香港理工大学博士后，西北工业大学教授、博导，曾担任西北工业大学应用数学系主任、中国工业与应用数学学会图论组合与应用分会秘书长、中国运筹学会图论组合分会常务理事、中国数学会组合数学与图论专业委员会理事和中国高等教育学会教育数学专业委员会常务理事。主持国家自然科学基金项目6项，发表学术论文100余篇。

Eigenvalue multiplicity in cubic signed graphs

侯耀平湖南师范大学

摘要: A signed graph consists of an unsigned graph and a sign function。In this talk, we will introduce some results on the eigenvalue multiplicity of signed graphs, we give a linear upper bound for eigenvalue multiplicity in cubic signed graphs and determined signed graphs for which the bounds are attained.

报告人简介:侯耀平，湖南师范大学教授，博士生导师。长期从事代数学和组合数学的教学与研究，主要研究领域为代数图论及其应用，已在European Journal of Combinatorics，Discrete Applied Mathematics，Linear Algebra and its Applications，Electronic Journal of Combinatorics等国内外知名学术期刊上发表论文90多篇。已主持国家自然科学基金项目多项，主持湖南省教育厅重点项目和优秀青年项目各一项，是湖南省高校科技创新团队项目“复杂网络中的典型数学问题研究”带头人。完成的科研成果2003年和2010年分别获得安徽省科技进步二等奖和湖南省人民政府自然科学奖二等奖。

On the extensional eigenvalues of graphs

冯立华中南大学

摘要: Let G be a graph on n vertices with associated symmetric matrices M and K of order n,  where K is positive definite. If there exists $0\ne x\in\mathbb{R}^n$ such that Mx=\lambda Kx, then \lambda is called an extensional eigenvalue of G with respect to K. This concept generalizes some classic graph eigenvalue problems of certain matrices such as the adjacency matrix, the Laplacian matrix, the diffusion matrix. In this paper, we study the extensional eigenvalues of graphs, we develop some basic theories about extensional eigenvalues, and present some connections between extensional eigenvalues and the structure of graphs.

报告人简介:冯立华，中南大学教授，博士生导师。2007年2月于上海交通大学获得博士学位，2014年9月评为教授。主要关注图论，代数图论，组合矩阵论以及设计等相关问题及其在物理化学中的应用。

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

晏卫根集美大学

摘要: For the monomer-dimer model on a graph in statistical physics, a monomer-dimer of is a spanning subgraph of G, each component of which is an edge (dimer) or an isolate vertex (monomer). In this talk, we first introduce some known results on the monomer-dimer problem. Then, by using a combinatorial technique (a combinatorial bijection), we obtain the exact solution of the monomer-dimer problem on a fractal scale-free lattice in the context of statistical physics.

This is joint work with Danyi Li and Shuli Li.

报告人简介：晏卫根，集美大学教授。研究方向为：组合数学与图论。在包括Journal of Combinatorial Theory Ser. A, Journal of Graph Theory, Advances in Applied Mathematics, Studies in Applied Mathematics, Theoretical Computer Science, Journal of Statistical Physics等10多种国际学术期刊上共发表学术论文50多篇，SCI他引超过400次。承担过4项国家自然科学基金面上项目的研究。2009年，获福建省科学技术奖（自然科学奖）一等奖。

Spectral extrema of graphs with given size

翟明清滁州学院

摘要: In 2013, Furedi and Simonovits proposed a generalized Turan-type problem: We have a graph family U and a graph H. We have some parameters on U. Our aim is to maximize the second parameter under the condition that G\in U is H-free and its first parameter is given.

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.

报告人简介:翟明清, 博士，滁州学院教授, 2010年博士毕业于华东师范大学。研究方向为图论、代数图论。主持并完成国家自然科学基金青年项目、安徽省自然科学基金青年项目。2013年被评为安徽省学术技术带头人后备人选，2018年被评为安徽省教学名师。

On the skew spectral moments of graphs

刘慧清湖北大学

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 $T(G^{\sigma}) = (T_0(G^{\sigma}), T_1(G^{\sigma}),…,T_{n−1}(G^{\sigma}))$ 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 ($1 \leq k \leq n−1$), $T_i(G_1^{\sigma_1}) = T_i(G_2^{\sigma_2})$ ($i = 0,1,…,k−1$) 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.

报告人简介:刘慧清，2004年博士毕业于中科院数学与系统科学研究院，同年获理学博士学位，2016年3月-2017年3月受国家留学基金委资助在美国佐治亚州立大学(Georgia State University)从事访问交流研究工作。自2004年以来，先后执教于南开大学、湖北大学，现为湖北大学数学与统计学学院教授／博士生导师。目前的主要研究兴趣集中在图的结构性质、图谱理论及其应用上，发表学术论文70余篇。主持国家自然科学基金面上项目3项，参与国家自然科学基金项目5项。

Polynomials and spectral radius of hypergraphs

李红海江西师范大学

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.

报告人简介:李红海，江西师范大学教授，博士生导师，中国工业与应用数学学会专业委员会委员。2007年于中国科技大学获博士学位,曾应邀访问香港理工大学数学系，受国家公派在加拿大西蒙佛雷泽大学访学一年。研究兴趣包括图谱理论和图的匹配理论，在Linear Alg. Appl., J. Comb. Opt.等学术期刊发表论文多篇，主持（含已结题）国家自然科学基金3项，获江西省杰出青年基金人才计划资助，江西省自然科学基金3项及教育厅自然科学基金2项。

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

radii of uniform hypergraphs

刘乐乐上海理工大学

摘要: Let G be an r-uniform hypergraph of order n. For each $p\geq 1$, the p-spectral radius $\lambda^{(p)}(G)$ is defined as

\[

\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.

报告人简介: 刘乐乐, 博士, 上海理工大学沪江博士后。2019年博士毕业于上海大学。主要研究方向为图论、图谱和超图谱理论、图论中的概率方法。目前主持国家自然科学基金青年项目一项。