Automorphisms of a distance-regular graph with intersection array $\{75,64,18,1;1,6,64,75\}$
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 23 (2017) no. 4, pp. 128-135
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A distance-regular graph $\Gamma$ with intersection array $\{115,96,30,1;1,10,96,175\}$ is an $AT4$-graph. The antipodal quotient $\Gamma'$ has parameters $(392,115,18,40)$, and its first and second neighborhoods of vertices are strongly regular with parameters $(115,18,1,3)$ and $(276,75,10,24)$. Moreover, the second neighborhood of any vertex in $\Gamma_2(u)$ has intersection array $\{75,64,18,1;1,6,64,75\}$ and is a $4$-cover of a strongly regular graph with parameters $(276,75,10,24)$. Earlier, Makhnev, Paduchikh, and Samoilenko found possible automorphisms of a graph with parameters $(392,115,18,40)$ and of a graph with intersection array $\{115,96,30,1;1,10,96,175\}$. In this paper we find automorphisms of a graph with intersection array $\{75,64,18,1;1,6,64,75\}$. It is proved that the automorphism group of this graph acts intransitively on the set of its antipodal classes.
Keywords:
distance-regular graph, automorphism of a graph.
@article{TIMM_2017_23_4_a12,
author = {A. Kh. Zhurtov and M. Kh. Shermetova},
title = {Automorphisms of a distance-regular graph with intersection array $\{75,64,18,1;1,6,64,75\}$},
journal = {Trudy Instituta matematiki i mehaniki},
pages = {128--135},
publisher = {mathdoc},
volume = {23},
number = {4},
year = {2017},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TIMM_2017_23_4_a12/}
}
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AU - A. Kh. Zhurtov
AU - M. Kh. Shermetova
TI - Automorphisms of a distance-regular graph with intersection array $\{75,64,18,1;1,6,64,75\}$
JO - Trudy Instituta matematiki i mehaniki
PY - 2017
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A. Kh. Zhurtov; M. Kh. Shermetova. Automorphisms of a distance-regular graph with intersection array $\{75,64,18,1;1,6,64,75\}$. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 23 (2017) no. 4, pp. 128-135. http://geodesic.mathdoc.fr/item/TIMM_2017_23_4_a12/