Geodesic
Automorphisms of the $AT4(6,6,3)$-graph and its strongly-regular graphs
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 10 (2017) no. 3, pp. 271-280.

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

Koolen and Jurisich defined class of $AT4$-graphs (tight antipodal graph of diameter $4$). Among these graphs available graph with intersection array $\{288,245,48,1;1,24,245,288\}$ on $v=1+288+2940+576+2=3807$ vertices. Antipodal quotient of this graph is strongly regular graph with parameters $(1269,288,42,72)$. Both these graphs are locally pseudo $GQ(7,5)$-graphs. In this paper we find possible automorphisms of these graphs. In particular, group of automorphisms of distance-regular graph with intersection array $\{288,245,48,1;1,24,245,288\}$ acts intransitive on the set of its antipodal classes.
Keywords: distance-regular graph, strongly-regular graph, automorphism of the graph. 
@article{JSFU_2017_10_3_a0,
     author = {Konstantin S. Efimov and Aleksandr A. Makhnev},
     title = {Automorphisms of the $AT4(6,6,3)$-graph and its strongly-regular graphs},
     journal = {\v{Z}urnal Sibirskogo federalʹnogo universiteta. Matematika i fizika},
     pages = {271--280},
     publisher = {mathdoc},
     volume = {10},
     number = {3},
     year = {2017},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JSFU_2017_10_3_a0/}
}
TY  - JOUR
AU  - Konstantin S. Efimov
AU  - Aleksandr A. Makhnev
TI  - Automorphisms of the $AT4(6,6,3)$-graph and its strongly-regular graphs
JO  - Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika
PY  - 2017
SP  - 271
EP  - 280
VL  - 10
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/JSFU_2017_10_3_a0/
LA  - en
ID  - JSFU_2017_10_3_a0
ER  - 
%0 Journal Article
%A Konstantin S. Efimov
%A Aleksandr A. Makhnev
%T Automorphisms of the $AT4(6,6,3)$-graph and its strongly-regular graphs
%J Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika
%D 2017
%P 271-280
%V 10
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/JSFU_2017_10_3_a0/
%G en
%F JSFU_2017_10_3_a0
Konstantin S. Efimov; Aleksandr A. Makhnev. Automorphisms of the $AT4(6,6,3)$-graph and its strongly-regular graphs. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 10 (2017) no. 3, pp. 271-280. http://geodesic.mathdoc.fr/item/JSFU_2017_10_3_a0/

[1] A. Jurisic, J. Koolen, “Classification of the family $AT4(qs,q,q)$ of antipodal tight graphs”, J. Comb. Theory, 118:3 (2011), 842–852 | DOI | MR | Zbl

[2] A. E. Brouwer, W. H. Haemers, Spectra of Graphs, Springer, New York, 2012 | MR | Zbl

[3] P. J. Cameron, Permutation Groups, London Math. Soc. Student Texts, 45, 1999 | MR | Zbl

[4] A. L. Gavrilyuk, A. A. Makhnev, “On automorphisms of a distance-regular graph with intersetion array $\{56,45,1;1,9,56\}$”, Doklady Akademii Nauk, 432:5 (2010), 512–515 (in Russian) | MR

[5] M. Behbahani, C. Lam, “Strongly regular graphs with non-trivial automorphisms”, Discrete Math., 311:3 (2011), 132–144 | DOI | MR | Zbl

[6] A. V. Zavarnitsine, “Finite simple groups with narrow prime spectrum”, Siberian Electr. Math. Reports, 6 (2009), 1–12 | MR | Zbl