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 ${\mathrm{VO}}_{2m}^{\epsilon }(2)$ 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 $T_{0,\ddot{I}‰}=T_{\ddot{I}}‰={\tilde{T}}_{\ddot{I}}‰$ of their Terwilliger algebras.

12 pages, comments are welcome