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

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Home Editorial board Publication ethics Peer review guidelines Latest issue All issues Rules for authors Online submission system's guidelines Submit manuscript Contacts Address: Vatutina st. 53, Vladikavkaz, 362025, RNO-A, Russia Phone: (8672)23-00-54 E-mail: rio@smath.ru	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. Abstract: 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 + References 1. Cameron P., Van Lint J. Designs, Graphs, Codes and their Links, Cambridge, Cambridge Univ. Press, 1981, 240 p. (London Math. Soc. Student Texts, no. 22). 2. Mahnev A. A. Rasshirenija simmetrichnyh 2-shem. Tez. Dokl. Mezhdunar. Konf. "Mal'cevskie Chtenija" [Collection of Abstracts International Conference "Mal'tsev Meeting"], Novosibirsk, 2015, p. 112 (Russian). 3. Brouwer A. E., Haemers W. H. The Gewirtz Graph: an Exercize in the Theory of Graph Spectra. Europ. J. Comb., 1993, vol. 14, pp. 397-407. 4. Behbahani M., Lam C. Strongly Regular Graphs with Non-Trivial Automorphisms. Discrete Math., 2011, vol. 311, no. 2-3, pp. 132-144. 5. Cameron P. J. Permutation Groups, Cambridge, Cambridge Univ. Press, 1999 (London Math. Soc. Student Texts, no. 45). 6. Gavriljuk A. L., Mahnev A. A. Ob avtomorfizmah distancionno reguljarnogo grafa s massivom peresechenij {56,45,1;1,9,56}. Dokl. AN [Doklady Mathematics], 2010, vol. 432, no. 5, pp. 512-515 (Russian). 7. Zavarnitsine A. V. Finite Simple Groups with Narrow Prime Spectrum. Sib. Electr. Math. Reports, 2009, vol. 6, pp. 1-12. The sole copyright holder of the published work is the Founder of the Vladikavkaz Mathematical Journal. The terms of use of this work are governed by an open license (Creative Commons Attribution-NonCommercial 4.0 International). The use of metadata of the scientific article, including the title, abstract, author information, references, identifiers, and other bibliographic description elements for subsequent unrestricted use, is carried out under the terms of the CC BY or CC0 open licenses. ← Contents of issue


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