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Automorphisms of a strongly regular graph with parameters \((1197,156,15,21)\). (Russian. English summary) Zbl 1474.05386

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.

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
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References:

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