Qianqian Yang

Affiliation:  Shanghai University

Title: On sesqui-regular graphs with fixed smallest eigenvalue 

Abstract: Let $\lambda\geq2$ be an integer. For strongly regular graphs with parameters $(v, k, a,c)$ and fixed smallest eigenvalue $-\lambda$, Neumaier gave two bounds on $c$ by using algebraic property of strongly regular graphs. Subsequently, we studied a new class of regular graphs called \emph{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 $-\lambda$, if $k$ is very large, then either $c \leq \lambda^2(\lambda -1)$ or $v-k-1 \leq \frac{(\lambda-1)^2}{4} + 1$. This is joint work with Jack Koolen, Brhane Gebremichel and Jae Young Yang.

You can watch the talk here, and the slides are available here.

This talk was given on September 12th, 2022