K. S. Efimov, A. A. Makhnev, “On automorphisms of a distance-regular graph with intersection array <nobr>$\{99,84,30;1,6,54\}$</nobr>”, Diskr. Mat., 2017, Volume 29, Issue 1,Pages <nobr>10

This article is cited in 2 papers

On automorphisms of a distance-regular graph with intersection array $\{99,84,30;1,6,54\}$

K. S. Efimov^a, A. A. Makhnev^b

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

Abstract: Recently it was shown that a distance-regular graph in which neighbourhoods of vertices are strongly regular with parameters (99,14,1,2) has intersection array $\{99,84,1;1,14,99\}$, $\{99,84,1;1,12,99\}$ or $\{99,84,30;1,6,54\}$. In the present paper we find possible automorphisms of a graph with the intersection array $\{99,84,30;1,6,54\}$. It is shown, in particular, that such a graph is not point-symmetric.

Keywords: distance-regular graph, strongly regular graph, automorphism of a graph.

UDC: 519.179.175.1

Received: 26.01.2016

DOI: 10.4213/dm1402