I. N. Belousov, “On automorphisms of a distance-regular graph with intersection array <nobr>$\{39,36,1;1,2,39\}$</nobr>”, Trudy Inst. Mat. i Mekh. UrO RAN, 2015, Volume 21, Number 3,Pages <nobr>54

On automorphisms of a distance-regular graph with intersection array $\{39,36,1;1,2,39\}$

I. N. Belousov^ab

^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: Possible prime-order automorphisms and fixed-point subgraphs are found for a hypothetical distance-regular graph with intersection array $\{39,36,1;1,2,39\}$. It is shown that graphs with intersection arrays $\{15,12,1;1,2\}$, $\{35,32,1;1,2,35\}$, and $\{39,36,1;1,2,39\}$ are not vertex-symmetric.

Keywords: distance-regular graph, graph automorphism.

UDC: 517.977

Received: 11.03.2015