A. A. Makhnev, V. I. Belousova, “Automorphisms of a distance-regular graph with intersection array <nobr>$\{45,42,1;1,6,45\}$</nobr>”, Sib. Èlektron. Mat. Izv., 2016, Volume 13,Pages <nobr>130

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Mathematical logic, algebra and number theory

Automorphisms of a distance-regular graph with intersection array $\{45,42,1;1,6,45\}$

A. A. Makhnev^a, V. I. Belousova^b

^a Institute of Mathematics and Mechanics UB RAS, S. Kovalevskoi 16, 620990, Yekaterinburg, Russia
^b Ural Federal University, Mira 16, 620000, Yekaterinburg, Russia

Abstract: Prime divisors of orders of automorphisms and the fixed point subgraphs of automorphisms of prime orders are studied for a hypothetical distance-regular graph with intersection array $\{45,42,1;1,6,45\}$. It is proved that this graph does not vertex-symmetric.

Keywords: distance-regular graph, automorphism group, antipodal cover.

UDC: 519.17

MSC: 05C25

Received January 13, 2016, published March 4, 2016

DOI: 10.17377/semi.2016.13.011