Automorphisms of the Cameron's monster with parameters (6138, 1197, 156, 252)

Bitkina, V. V.
Vladikavkaz Mathematical Journal 2017. Vol. 19. Issue 1.

Abstract:
Let the \(3\)-\((V, K, \Lambda)\) scheme \(E=(X,B)\) be an extension of the symmetric 2-scheme. Then either \(E\) 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 \((6138,1197,156,252).\) Let's call this complementary graph Cameron's monster. In this paper automorphisms of monster are studied.Let the \(3\)-\((V, K, \Lambda)\) scheme \(E=(X,B)\) is an extension of the symmetric 2-scheme. Then either \(E\) 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 \((6138,1197,156,252).\) Let's call this complementary graph Cameron's monster. In this paper automorphisms of monster are studied.

Keywords: strongly regular graph, vertex symmetric graph, automorphism group of a graph

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