Geodesic
On automorphisms of distance-regular graphs with intersection arrays $\{2r+1,2r-2,1;1,2,2r+1\}$
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 22 (2016) no. 2, pp. 28-37

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

Let $\Gamma$ be an antipodal graph with intersection array $\{2r+1,2r-2,1;1,2,2r+1\}$, where $2r(r+1)\le 4096$. If $2r+1$ is a prime power, then Mathon's scheme provides the existence of an edge-symmetric graph with this intersection array. Note that $2r+1$ is not a prime power only for $r\in \{7,17,19,22,25,27,31,32,37,38,42,43\}$. We study automorphisms of hypothetical distance-regular graphs with the specified values of $r$. The cases $r\in \{7,17,19\}$ were considered earlier. We prove that, if $\Gamma$ is a vertex-symmetric graph with intersection array $\{2r+1,2r-2,1;1,2,2r+1\}$, $2r+1$ is not a prime power, and $r\le 43$, then $r=25,27,31$.
Keywords: distance-regular graph
Mots-clés : graph automorphism. 
@article{TIMM_2016_22_2_a3,
     author = {I. N. Belousov and A. A. Makhnev},
     title = {On automorphisms of distance-regular graphs with intersection arrays $\{2r+1,2r-2,1;1,2,2r+1\}$},
     journal = {Trudy Instituta matematiki i mehaniki},
     pages = {28--37},
     publisher = {mathdoc},
     volume = {22},
     number = {2},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TIMM_2016_22_2_a3/}
}
TY  - JOUR
AU  - I. N. Belousov
AU  - A. A. Makhnev
TI  - On automorphisms of distance-regular graphs with intersection arrays $\{2r+1,2r-2,1;1,2,2r+1\}$
JO  - Trudy Instituta matematiki i mehaniki
PY  - 2016
SP  - 28
EP  - 37
VL  - 22
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TIMM_2016_22_2_a3/
LA  - ru
ID  - TIMM_2016_22_2_a3
ER  - 
%0 Journal Article
%A I. N. Belousov
%A A. A. Makhnev
%T On automorphisms of distance-regular graphs with intersection arrays $\{2r+1,2r-2,1;1,2,2r+1\}$
%J Trudy Instituta matematiki i mehaniki
%D 2016
%P 28-37
%V 22
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TIMM_2016_22_2_a3/
%G ru
%F TIMM_2016_22_2_a3
I. N. Belousov; A. A. Makhnev. On automorphisms of distance-regular graphs with intersection arrays $\{2r+1,2r-2,1;1,2,2r+1\}$. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 22 (2016) no. 2, pp. 28-37. http://geodesic.mathdoc.fr/item/TIMM_2016_22_2_a3/