讲座内容：

This report explores the development and applications of the $\alpha$-normal labelling method and its extension, the $(\alpha, \beta)$-labelling method, in $k$-uniform hypergraphs and graphs. Initially proposed by Linyuan Lu and Shoudong Man in their 2016 paper, this method has significantly advanced the study 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 to gain deeper insights into their spectral properties. This method has been instrumental in identifying hypergraph structures with minimal spectral radii.

Recent research has further explored the spectral radius in specific types of hypergraphs, such as bicyclic uniform hypergraphs, and developed necessary conditions for extremal graph structures. Additionally, the method has been applied to degree-based weighted adjacency matrices in graphs, enabling the determination of extremal spectral radii for graphs with given order and size.

These advancements have expanded the theoretical framework of hypergraph and graph spectral theory, providing essential tools for both theoretical analysis and practical applications. The continued development of these labelling methods underscores their importance and versatility in advancing the field of graph theory.