Abstract
Automorphisms of distance-regular graphs are considered. It is proved that any graph with the intersection array {60, 45, 8; 1, 12, 50} is not vertex symmetric, and any graph with the intersection array {49, 36, 8; 1, 6, 42} is not edge symmetric.
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A. E. Brouwer, A. M. Cohen, and A. Neumaier, Distance-Regular Graphs, in Ergeb. Math. Grenzgeb. (3) (Springer-Verlag, Berlin, 1989), Vol. 18.
P. J. Cameron and J. H. van Lint, Designs, Graphs, Codes and Their Links, in London Math. Soc. Stud. Texts (Cambridge Univ. Press, Cambridge, 1991), Vol. 22.
A. L. Gavrilyuk and A. A. Makhnev, “Amply regular graphs and block designs,” Sib. Mat. Zh. 47 (4), 753–768 (2006) [Sib. Math. J. 47 (4), 621–633 (2006)].
A. L. Gavrilyuk and A. A. Makhnev, “Automorphisms of a distance-regular graph with the intersection array {60, 45, 8; 1, 12, 50},” Tr. IMM UrO RAN 13 (3), 41–53 (2007).
A. L. Gavrilyuk and A. A. Makhnev, “On automorphisms of distance-regular graphs with intersection array {56, 45, 1; 1, 9, 56},” Dokl. Ross. Akad. Nauk 432 (5), 583–587 (2010) [Dokl. Math. 81 (3), 439–442 (2010)].
A. V. Zavarnitsine, “Finite simple groups with narrow prime spectrum,” Sib. Élektron. Mat. Izv. 6, 1–12 (2009).
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Original Russian Text © A. L. Gavrilyuk, A. A. Makhnev, 2017, published in Matematicheskie Zametki, 2017, Vol. 101, No. 6, pp. 823–831.
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Gavrilyuk, A.L., Makhnev, A.A. Automorphisms of graphs with intersection arrays {60, 45, 8; 1, 12, 50} and {49, 36, 8; 1, 6, 42}. Math Notes 101, 942–950 (2017). https://doi.org/10.1134/S0001434617050200
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DOI: https://doi.org/10.1134/S0001434617050200