On the combinatorial structure of graphs with a spectral idempotent of small dual diameter

Edwin R. van Dam, Giusy Monzillo, Safet Penjić

Let $\Gamma$ be a connected regular graph with an eigenvalue $\lambda$ and corresponding idempotent $E_{\lambda }$. Let ${\mathcal{E}}_{\lambda }=⟨J,E_{\lambda }{⟩}^{\circ }$ be the algebra generated by $J$ and $E_λ…