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Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2009, Volume 15, Number 2, Pages 162–176
(Mi timm232)
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This article is cited in 2 scientific papers (total in 3 papers)
On the automorphism group of the Aschbacher graph
A. A. Makhnev, D. V. Paduchikh Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences
Abstract:
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).
Keywords:
automorphism group of a graph, Moore graph, strongly regular graph.
Received: 10.12.2008
Citation:
A. A. Makhnev, D. V. Paduchikh, “On the automorphism group of the Aschbacher graph”, Trudy Inst. Mat. i Mekh. UrO RAN, 15, no. 2, 2009, 162–176; Proc. Steklov Inst. Math. (Suppl.), 267, suppl. 1 (2009), S149–S163
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https://www.mathnet.ru/eng/timm232 https://www.mathnet.ru/eng/timm/v15/i2/p162
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Abstract page: | 523 | Full-text PDF : | 125 | References: | 62 | First page: | 4 |
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