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DOI: 10.23671/VNC.2017.1.5816

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

Bitkina, V. V.
Vladikakazian 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