【和山数学论坛265期】盐城师范学院郭曙光教授学术报告

题目：Ordering graphs by their largest (least) A_alphaeigenvalues

主讲人：盐城师范学院郭曙光教授

时间：2021年12月26日(周日)8:30~9:15

腾讯会议：871 251 058（会议密码：654321）

摘要：

Let G be a simple undirected graph. For real number alpha in [0,1]. Nikiforov defined the A_{alpha} matrix of G as A_{alpha}(G)=alpha D(G)+(1-alpha)A(G), where A(G) and D(G) are the adjacency matrix and the degree diagonal matrix of $G$ respectively.

In this talk, we present a sharp upper bound on the largest eigenvalue \rho_{alpha}(G) of A_{alpha}(G) for alpha in [1/2, 1). Employing this upper bound, we prove that: For connected G₁and G₂with n vertices and m edges, if the maximum degree $\Delta(G₁)>2alpha(1-alpha)(2mn+1)+2 alpha and Delta(G₁)>Delta(G₂), then \rho_{alpha}(G₁)>\rho_\alpha(G₂)$.

Let lambda_{alpha}(G) denote the least eigenvalue of A_{alpha}(G). For alpha in (1/2, 1), we prove that: For two connected G₁and G₂, if the minimum degree delta(G₁)<\frac{1}{1-\alpha}-2 and delta(G₁)₂), then lambda_{alpha}( G₁)₂).

个人简介：郭曙光，男，博士，江苏省盐城师范学院教授，主要从事代数图论和组合数论的研究，曾被评为江苏省高校“青蓝工程”中青年学术带头人和江苏省“333工程”培养对象，先后主持国家自然科学基金面上项目2项，江苏省自然科学基金面上项目2项，在《J. Number Theory》《Linear Algebra Appl.》《Discrete Math.》等重要学术刊物上发表论文50余篇，出版江苏省高等学校重点教材1部，获江苏省教育科学研究成果二等奖1项。

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