主 讲 人 ：​单海英    教授

活动时间：2025-08-03 15:30:00

地      点 ：理科群1号楼D204室

主办单位：数学科学学院

讲座内容：

This reportexplores the development and applications of the $\alpha$-normal labellingmethod and its extension, the $(\alpha, \beta)$-labelling method, in$k$-uniform hypergraphs and graphs. Initially proposed by Linyuan Lu andShoudong Man in their 2016 paper, this method has significantly advanced thestudy of spectral properties in hypergraphs.

The$\alpha$-normal labelling method has been extended to the $(\alpha,\beta)$-labelling method, which has been applied to $k$-uniform hypergraphs togain deeper insights into their spectral properties. This method has beeninstrumental in identifying hypergraph structures with minimal spectral radii.

Recent researchhas further explored the spectral radius in specific types of hypergraphs, suchas bicyclic uniform hypergraphs, and developed necessary conditions forextremal graph structures. Additionally, the method has been applied todegree-based weighted adjacency matrices in graphs, enabling the determinationof extremal spectral radii for graphs with given order and size.

These advancements haveexpanded the theoretical framework of hypergraph and graph spectral theory,providing essential tools for both theoretical analysis and practicalapplications. The continued development of these labelling methods underscorestheir importance and versatility in advancing the field of graph theory.

主讲人介绍：

单海英，同济大学数学科学学院，教授，博士生导师，主要从事组合矩阵论和代数图论的研究，至今在DM，DAM, LAA, LMA 等国际期刊上发表科研论文 60余篇。曾先后主持国家自然科学面上基金、国家自然科学青年基金、中央高校基本科研业务项目等多项科研课题。