Bitkina, Viktoriya Vasil’evna; Gutnova, Alina Kazbekovna; Makhnev, Aleksandr Alekseevich Automorphisms of a strongly regular graph with parameters \((1197,156,15,21)\). (Russian. English summary) Zbl 1474.05386 Vladikavkaz. Mat. Zh. 17, No. 2, 5-11 (2015). Summary: Let a 3-\((V,K,\Lambda)\) scheme \(\mathscr{E}=(X,\mathscr{B})\) is an extension of a symmetric 2-scheme. Then either \(\mathscr{E}\) is Hadamard 3-\((4\Lambda+4,2\Lambda+2,\Lambda)\) scheme, or \(V=(\Lambda+1)(\Lambda^2+5\Lambda+5)\) and \(K=(\Lambda+1)(\Lambda+2)\), or \(V=496\), \(K=40\) and \(\Lambda=3\). The complementary graph of a block graph of 3-\((496,40,3)\) scheme is strongly regular with parameters \((6138,1197,156,252)\) and the neighborhoods of its vertices are strongly regular with parameters \((1197,156,15,21)\). In this paper automorphisms of strongly regular graph with parameters \((1197,156,15,21)\) are studied. We yet introduce the structure of automorphism groups of abovementioned graph in vetrex symmetric case. Cited in 1 Document MSC: 05E30 Association schemes, strongly regular graphs 05C25 Graphs and abstract algebra (groups, rings, fields, etc.) 20B25 Finite automorphism groups of algebraic, geometric, or combinatorial structures 05B05 Combinatorial aspects of block designs Keywords:strongly regular graph; vertex symmetric graph; automorphism groups of graph PDFBibTeX XMLCite \textit{V. V. Bitkina} et al., Vladikavkaz. Mat. Zh. 17, No. 2, 5--11 (2015; Zbl 1474.05386) Full Text: MNR References: [1] Cameron P., Van Lint J., Designs, Graphs, Codes and their Links, London Math. Soc. Student Texts, 22, Cambridge Univ. Press, Cambridge, 1981, 240 pp. · Zbl 0743.05004 [2] Makhnev A. A., “Rasshireniya simmetrichnykh 2-skhem”, Tez. dokl. mezhdunar. konf. “Maltsevskie chteniya”, Novosibirsk, 2015, 112 [3] Brouwer A. E., Haemers W. H., “The Gewirtz graph: an exercize in the theory of graph spectra”, Europ. J. Comb., 14 (1993), 397-407 · Zbl 0794.05076 · doi:10.1006/eujc.1993.1044 [4] Behbahani M., Lam C., “Strongly regular graphs with non-trivial automorphisms”, Discrete Math., 311:2-3 (2011), 132-144 · Zbl 1225.05248 · doi:10.1016/j.disc.2010.10.005 [5] Cameron P. J., Permutation Groups, London Math. Soc. Student Texts, 45, Cambridge Univ. Press, Cambridge, 1999 · Zbl 0922.20003 [6] Gavrilyuk A. L., Makhnev A. A., “Ob avtomorfizmakh distantsionno regulyarnogo grafa s massivom peresechenii \(\{56,45,1;1,9,56\}\)”, Dokl. AN, 432:5 (2010), 512-515 [7] Zavarnitsine A. V., “Finite simple groups with narrow prime spectrum”, Sib. electr. Math. Reports, 6 (2009), 1-12 · Zbl 1289.20021 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.