On the automorphism group of the Aschbacher graph
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 15 (2009) no. 2, pp. 162-176
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A Moore graph is a regular graph of degree $k$ and diameter $d$ with $v$ vertices such that $v\le1+k+k(k-1)+\dots+k(k-1)^{d-1}$. It is known that a Moore graph of degree $k\ge3$ has diameter 2, i.e., it is strongly regular with parameters $\lambda=0$, $\mu=1$ and $v=k^2+1$, where the degree $k$ is equal to 3, 7, or 57. It is unknown whether there exists a Moore graph of degree $k=57$. Aschbacher showed that a Moore graph with $k=57$ is not a graph of rank 3. In this connection, we call a Moore graph with $k=57$ the Aschbacher graph and investigate its automorphism group $G$ without additional assumptions (earlier, it was assumed that $G$ contains an involution).
Mots-clés :
automorphism group of a graph
Keywords: Moore graph, strongly regular graph.
Keywords: Moore graph, strongly regular graph.
@article{TIMM_2009_15_2_a14,
author = {A. A. Makhnev and D. V. Paduchikh},
title = {On the automorphism group of the {Aschbacher} graph},
journal = {Trudy Instituta matematiki i mehaniki},
pages = {162--176},
publisher = {mathdoc},
volume = {15},
number = {2},
year = {2009},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TIMM_2009_15_2_a14/}
}
A. A. Makhnev; D. V. Paduchikh. On the automorphism group of the Aschbacher graph. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 15 (2009) no. 2, pp. 162-176. http://geodesic.mathdoc.fr/item/TIMM_2009_15_2_a14/