学术报告-黄琼湘

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2021-05-05 08:16:00

学术报告


题      目: Quadratic starlike trees


报  告  人:黄琼湘   教授  (邀请人:周波 )

                                   新疆大学



时      间:2021-05-05  09:00--10:00


地      点:学院401


报告人简介:

       新疆大学数学与系统科学学院教授、博士生导师,主要研究领域为图论、代数图论、图谱理论。主持多项国家自然科学基金项目, 参加国家自然科学基金重点项目。在J.
Combin.Theory Ser. B、J. Algebraic Algebra、Discrete Math.、 Linear Algebra
Appl.等国内外重要专业期刊发表论文140多篇。获新疆维吾尔自治区科技进步奖二等奖。


摘      要:

       Harary and Schwenk in [Harary, F., Schwenk, A.J.: Which graphs have integral spectra? in Graphs and Combinatorics. Lecture Notes in Math, vol. 406. Springer, Berlin (1974)] proposed to classify integral graphs about 40 year ago. This problem initiates a significant investigation among algebraic graph theorists. It turns out to be extremely hard although this problem is easy to state. One can refer to [Lu Lu, Qiongxiang Huang and Xueyi Huang, Integral Cayley graphs over dihedral groups, J Algebr Comb, (2017)] for the summary of the researches of integral graphs. Here we extend the notion of integral graph and define the quadratic graph, that is a graph whose eigenvalues are integral or quadratic algebraic integral. In this talk, we will introduce some notion and method to identify the the quadratic graphs, and focus to determine nine infinite families of quadratic starlike trees including integral starlike trees. Thus the quadratic starlike trees are completely characterized.