Geodesic
On the automorphisms of the strongly regular graph with parameters $(85, 14, 3, 2)$
Diskretnaya Matematika, Tome 21 (2009) no. 1, pp. 78-104 
D. V. Paduchikh. On the automorphisms of the strongly regular graph with parameters $(85, 14, 3, 2)$. Diskretnaya Matematika, Tome 21 (2009) no. 1, pp. 78-104. http://geodesic.mathdoc.fr/item/DM_2009_21_1_a4/
@article{DM_2009_21_1_a4,
     author = {D. V. Paduchikh},
     title = {On the automorphisms of the strongly regular graph with parameters $(85, 14, 3, 2)$},
     journal = {Diskretnaya Matematika},
     pages = {78--104},
     year = {2009},
     volume = {21},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DM_2009_21_1_a4/}
}
TY  - JOUR
AU  - D. V. Paduchikh
TI  - On the automorphisms of the strongly regular graph with parameters $(85, 14, 3, 2)$
JO  - Diskretnaya Matematika
PY  - 2009
SP  - 78
EP  - 104
VL  - 21
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/DM_2009_21_1_a4/
LA  - ru
ID  - DM_2009_21_1_a4
ER  - 
%0 Journal Article
%A D. V. Paduchikh
%T On the automorphisms of the strongly regular graph with parameters $(85, 14, 3, 2)$
%J Diskretnaya Matematika
%D 2009
%P 78-104
%V 21
%N 1
%U http://geodesic.mathdoc.fr/item/DM_2009_21_1_a4/
%G ru
%F DM_2009_21_1_a4

Voir la notice de l'article provenant de la source Math-Net.Ru

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.

[1] Makhnev A. A., Paduchikh D. V., “Ob avtomorfizmakh grafa Ashbakhera”, Algebra i logika, 40:2 (2001), 125–134 | MR | Zbl

[2] Brouwer A. E., Cohen A. M., Neumaier A., Distance-regular graphs, Springer, Berlin, 1989 | MR | Zbl

[3] Makhnev A. A., Nosov V. V., “Ob avtomorfizmakh silno regulyarnykh grafov s $\lambda=1$, $\mu=2$”, Matem. sbornik, 195:3 (2004), 47–68 | MR | Zbl

[4] Makhnev A. A., Minakova I. M., “Ob avtomorfizmakh grafov s $\lambda=1$, $\mu=2$”, Diskretnaya matematika, 16:1 (2004), 95–104 | MR | Zbl

[5] Brouwer A. E., Haemers W. H., “The Gewirtz graph: an exercise in the theory of graph spectra”, European J. Comb., 14 (1993), 397–407 | DOI | MR | Zbl

[6] Makhnev A. A., Paduchikh D. V., “O silnoi regulyarnosti nekotorykh reberno regulyarnykh grafov”, Algebra, logika i kibernetika, Tezisy dokladov, Irkutskii gosuniversitet, Irkutsk, 2004, 181–183

[7] Walter J., “The characterization of finite groups with Abelian Sylov 2-subgroups”, Ann. Math., 89 (1969), 405–514 | DOI | MR | Zbl

[8] Bombieri E., “Thompson's problem $(\sigma^2=3)$”, Invent. Math., 58 (1980), 77–100 | DOI | MR | Zbl

[9] Cameron P., Permutation groups, Cambridge Univ. Press, Cambridge, 1999 | MR