3 problems

Let $G$ be an amply regular graph with parameters $(n,d,\alpha,\beta)$, and let $\operatorname{diam}(G)$ denote its diameter. Diameter bound conjecture. When $\alpha=\beta=2$, the…

Let $G$ be a connected amply regular graph with parameters $(n,d,\alpha,\beta)$, and let $0<\varepsilon<1$ be a real number. Qiao, Park and Koolen's conjecture. There exists a cons…

Let $G$ be an amply regular graph with parameters $(n,d,\alpha,\beta)$, where $n$ is possibly infinite. Terwilliger's conjecture. If $\beta\geq 2$, then $G$ is finite. Terwilliger'…