The complete classification of triply-transitive strongly regular graphs

Abstract

This paper completes the classification of triply-transitive strongly regular graphs, a program recently initiated by Herman, Maleki, and Razafimahatratra. By proving that the collinearity graph of the polar space $\mathcal{Q}^{-}(5,q)$ and the affine polar graph $\mathrm{VO}^{\varepsilon}_{2m}(2)$ are triply-transitive, we resolve the final open cases in the classification. The result is a definitive list of all strongly regular graphs that exhibit this exceptional form of local symmetry, characterized by the equality $T_{0,\omega}=T_{\omega}=\widetilde{T}_{\omega}$ of their Terwilliger algebras.