On the automorphisms of the strongly regular graph with parameters $(85, 14, 3, 2)$

D. V. Paduchikh

Diskretnaya Matematika, Tome 21 (2009) no. 1, pp. 78-104

Résumé

Let $\Gamma$ be the strongly regular graph with parameters $(85, 14, 3, 2)$, $g$ be an element of prime order $p$ of $\operatorname{Aut}(\Gamma)$ and $\Delta=\operatorname{Fix}(g)$. In this paper, it is proved that either $p=5$ or $p=17$ and $\Delta$ is the empty graph, or $p=7$ and $\Delta$ is a 1-clique, or $p=5$ and $\Delta$ is a 5-clique, or $p=3$ and $\Delta$ is a quadrangle or a $2\times5$ lattice, or $p=2$ and $\Delta$ is a union of $\varphi$ isolated vertices and $\psi$ isolated triangles, $\psi=1$ and $\varphi\in\{4,6\}$ or $\psi=0$ and $\varphi=5$. In addition, it is shown that the graph $\Gamma$ is not vertex transitive.