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DOI: 10.23671/VNC.2015.2.7270

Automorphisms of a strongly regular graph with parameters \((1197, 156, 15, 21)\)

Bitkina, V. V. , Gutnova A. K. , Makhnev A. A.
Vladikavkaz Mathematical Journal 2015. Vol. 17. Issue 2.
Let a \(3\)-\((V,K,\Lambda)\) scheme \({\cal E}=(X,{\cal B})\) is an extension of a symmetric \(2\)-scheme. Then either \({\cal E}\) 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.
Keywords: strongly regular graph, vertex symmetric graph, automorphism groups of graph
Language: Russian Download the full text  
For citation: Bitkina V. V., Gutnova A. K., Makhnev A. A. Automorphisms of a strongly regular graph with parameters \((1197, 156, 15, 21)\). Vladikavkazskii matematicheskii zhurnal [Vladikavkaz Math. J.], vol. 17, no. 2, pp.5-11. DOI 10.23671/VNC.2015.2.7270
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