Automorphisms of small graphs with intersection array {nm-1, nm-n+m-1,n-m+1;1,1,nm-n+m-1}

摘要

Let ?? be a distance regular graph of diameter 3 for which the graph ??3 is a pseudo-network. Previously, A.A. Makhnev, M.P. Golubyatnikov, Wenbin Guo found infinite series of admissible arrays of intersections of such graphs. In the case of c2 = 1, we have the two-parameter series fnm??1;nm??n+m?? 1; n ?? m + 1; 1; 1;nm ?? n + m ?? 1g. Possible automorphisms of such graphs were found by A.A. Makhnev, M.P. Golubyatnikov. In this paper the author found automorphism groups of distance regular graphs with intersection arrays f90; 84; 7; 1; 1; 84g (n = 13;m = 7), f220; 216; 5; 1; 1; 216g (n = 17;m = 13), f272; 264; 9; 1; 1; 264g (n = 21;m = 13). In particular, this graphs are not arc transitive.