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Title: On sesqui-regular graphs with fixed smallest eigenvalue

Speaker: Qianqian Yang Affiliation: Shanghai University Location: Contact Sabrina Lato for Zoom link

Abstract: Let λ ≥ 2 be an integer. For strongly regular graphs with parameters (v, k, a, c) and fixed smallest eigenvalue −λ, Neumaier gave two bounds on c by using algebraic property of strongly regular graphs. Subsequently, we studied a new class of regular graphs called sesqui-regular graphs, which contains strongly regular graphs as a subclass, and proved that for a given sesqui-regular graph with parameters (v, k, c) and smallest eigenvalue −λ, if k is very large, then either c ≤ λ² (λ − 1) or v − k − 1 ≤ (λ−1)²/4 + 1. This is joint work with Jack Koolen, Brhane Gebremichel and Jae Young Yang