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Trudy Inst. Mat. i Mekh. UrO RAN, 2016, Volume 22, Number 2, Pages 28–37 (Mi timm1287)  

On automorphisms of distance-regular graphs with intersection arrays $\{2r+1,2r-2,1;1,2,2r+1\}$

I. N. Belousovab, A. A. Makhnevab

a Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, Ekaterinburg
b Ural Federal University named after the First President of Russia B. N. Yeltsin, Ekaterinburg

Abstract: 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, graph automorphism.

Funding Agency Grant Number
Russian Science Foundation 14-11-00061
Ministry of Education and Science of the Russian Federation 02.А03.21.0006


DOI: https://doi.org/10.21538/0134-4889-2016-22-2-28-37

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English version:
Proceedings of the Steklov Institute of Mathematics (Supplementary issues), 2017, 296, suppl. 1, 85–94

Bibliographic databases:

UDC: 519.17
MSC: 05C25
Received: 25.01.2016

Citation: 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 Inst. Mat. i Mekh. UrO RAN, 22, no. 2, 2016, 28–37; Proc. Steklov Inst. Math. (Suppl.), 296, suppl. 1 (2017), 85–94

Citation in format AMSBIB
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\vol 22
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\pages 28--37
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