2021年圖譜與超圖的張量譜理論研討會

2021年圖譜與超圖的張量譜理論研討會

為了加強圖譜與超圖的張量譜理論的學術交流，促進同行之間學術研究水平的提升，上海理工大學和同濟大學聯合於2021年4月24日舉辦線上“圖譜與超圖的張量譜理論”研討會。會議將圍繞圖譜和超圖的張量譜等領域的問題，深入探討譜理論的最新研究成果及其在各領域的應用。研討會的主旨是研究成果交流、國內外研究動態介紹和評述等。

會議的具體事宜如下：

1、會議時間：2021年4月24日，

2、報告安排：邀請每位參會老師做報告🥈，報告時間為40分鐘🎟，

3🦌、騰訊會議ID𓀋：693 826 297。

聯系人：何常香：changxiang-he@163.com

  劉樂樂：ahhylau@163.com

  吳寶豐：baufern@aliyun.com

  邵嘉裕：jyshao@tongji.edu.cn

會議日程(2021/04/24)

題目與摘要

The extremal graphs of order trees and their topological indices

黃瓊湘  新疆大學

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 <T_n,\preceq>. 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 <T_n,\preceq> and give a criterion to determine its order, which enable us to get the common extremal graphs in four prescribed subclasses of <T_n,\preceq>. 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 <C(n,k),\preceq>, <T_n(q),\preceq> and <T_n^\Delta,\preceq>.

報告人簡介:黃瓊湘，新疆大學數學與系統科學必一教授，博士生導師。近年來主要從事代數圖論，特別是圖譜理論的研究。主持完成重點項目子項目 1 項📞🏃🏻‍♂️‍➡️，國家自然科學基金3項。在 J. Combin. Theory Ser. B，Europ. J. Combin.🪝，Electronic Journal of Combinatorics，J. Algebraic Combin.，Discrete Math.✌🏼， Discrete Appl. Math.，Linear Algebra Appl. 等主流學術期刊上發表論文 120 余篇🐔。

代數連通度在多智能體系統一致性研究中的應用

張勝貴西北工業大學

摘要:本報告主要介紹圖的代數連通度在多智能體系統一致性問題研究中的重要應用. 通信網絡的代數連通度決定了一致性協議的收斂速度: 代數連通度越大, 一致性協議的收斂速度越快. 而且, 通信網絡的代數連通度對多智能體系統的通信量、通信延遲上限等都有影響: 對有通信時延的一致性協議, 代數連通度越大, 系統可允許較大的通信時延; 對周期通信和事件觸發的一致性協議, 代數連通度越大, 智能體間的通信頻率可以更低, 系統達成一致需要的通信量更少. 同時, 本報告將總結優化代數連通度的各種方法, 並提出了若幹待解決的問題.

報告人簡介:張勝貴👩🏼🫀，荷蘭Twente大學博士，香港理工大學博士後，西北工業大學教授、博導，曾擔任西北工業大學應用數學系主任、中國工業與應用數學學會圖論組合與應用分會秘書長😲、中國運籌學會圖論組合分會常務理事、中國數學會組合數學與圖論專業委員會理事和中國高等教育學會教育數學專業委員會常務理事。主持國家自然科學基金項目6項🤸🏻‍♀️，發表學術論文100余篇。

Eigenvalue multiplicity in cubic signed graphs

侯耀平湖南師範大學

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.

報告人簡介:侯耀平📹，湖南師範大學教授🏆🏚，博士生導師。長期從事代數學和組合數學的教學與研究，主要研究領域為代數圖論及其應用，已在European Journal of Combinatorics，Discrete Applied Mathematics，Linear Algebra and its Applications，Electronic Journal of Combinatorics等國內外知名學術期刊上發表論文90多篇🤵🏿‍♀️☎。已主持國家自然科學基金項目多項，主持湖南省教育廳重點項目和優秀青年項目各一項，是湖南省高校科技創新團隊項目“復雜網絡中的典型數學問題研究”帶頭人🍗。完成的科研成果2003年和2010年分別獲得安徽省科技進步二等獎和湖南省人民政府自然科學獎二等獎🔑。

On the extensional eigenvalues of graphs

馮立華中南大學

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.

報告人簡介:馮立華，中南大學教授，博士生導師。2007年2月於上海交通大學獲得博士學位🏉，2014年9月評為教授🧚🏿‍♂️🧖🏼。主要關註圖論🐋，代數圖論，組合矩陣論以及設計等相關問題及其在物理化學中的應用🧑🏻‍🦯‍➡️。

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

晏衛根集美大學

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.

報告人簡介：晏衛根，集美大學教授。研究方向為⛽️：組合數學與圖論。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多種國際學術期刊上共發表學術論文50多篇，SCI他引超過400次。承擔過4項國家自然科學基金面上項目的研究🗓😷。2009年，獲福建省科學技術獎（自然科學獎）一等獎。

Spectral extrema of graphs with given size

翟明清滁州必一

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.

報告人簡介:翟明清, 博士，滁州必一教授, 2010年博士畢業於華東師範大學。研究方向為圖論👩🏼‍🍳👍🏻、代數圖論。主持並完成國家自然科學基金青年項目、安徽省自然科學基金青年項目。2013年被評為安徽省學術技術帶頭人後備人選💁🏼‍♂️🧘🏻‍♀️，2018年被評為安徽省教學名師🧝🏿‍♀️💮。

On the skew spectral moments of graphs

劉慧清湖北大學

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.

報告人簡介:劉慧清，2004年博士畢業於中科院數學與系統科學研究院，同年獲理學博士學位➿，2016年3月-2017年3月受國家留學基金委資助在美國佐治亞州立大學(Georgia State University)從事訪問交流研究工作。自2004年以來，先後執教於南開大學🤷🏿‍♂️、湖北大學🛌🏽8️⃣，現為湖北大學數學與統計學必一教授／博士生導師。目前的主要研究興趣集中在圖的結構性質、圖譜理論及其應用上，發表學術論文70余篇。主持國家自然科學基金面上項目3項📷，參與國家自然科學基金項目5項🌘。

Polynomials and spectral radius of hypergraphs

李紅海江西師範大學

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.

報告人簡介:李紅海👲🏻，江西師範大學教授，博士生導師，中國工業與應用數學學會專業委員會委員。2007年於中國科技大學獲博士學位,曾應邀訪問香港理工大學數學系🫲🏿，受國家公派在加拿大西蒙佛雷澤大學訪學一年👈🏽。研究興趣包括圖譜理論和圖的匹配理論，在Linear Alg. Appl., J. Comb. Opt.等學術期刊發表論文多篇🦸🏿‍♂️，主持（含已結題）國家自然科學基金3項🎸，獲江西省傑出青年基金人才計劃資助🧯，江西省自然科學基金3項及教育廳自然科學基金2項🏄🏿‍♀️。

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

radii of uniform hypergraphs

劉樂樂上海理工大學

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.

報告人簡介: 劉樂樂, 博士, 上海理工大學滬江博士後🫱🏻。2019年博士畢業於上海大學。主要研究方向為圖論👇🏽⚗️、圖譜和超圖譜理論、圖論中的概率方法。目前主持國家自然科學基金青年項目一項🛼👷‍♂️。