AUTOMORPHISMS OF DISTANCE-REGULAR GRAPH WITH INTERSECTION ARRAY {39; 36; 4; 1; 1; 36}

Konstantin S. Efimov     (Ural State University of Economics, 62 March 8th Str., Ekaterinburg, 620144, Russian Federation)
Aleksandr A. Makhnev     (Krasovskii Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, 16 S. Kovalevskaya Str., Ekaterinburg, 620990, Russian Federation)

Abstract


Makhnev and Nirova have found intersection arrays of distance-regular graphs with no more than \(4096\) vertices, in which \(\lambda=2\)  and \(\mu=1\). They proposed the program of investigation of distance-regular graphs with \(\lambda=2\) and \(\mu=1\). In this paper the automorphisms of a distance-regular graph with intersection array \(\{39,36,4;1,1,36\}\) are studied.


Keywords


Strongly regular graph, Distance-regular graph

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References


  1. Brouwer A.E., Cohen A.M., Neumaier A. Distance-Regular Graphs. New York: Springer-Verlag, 1989. 495 p. DOI: 10.1007/978-3-642-74341-2
  2. Makhnev A.A., Nirova M.S. On distance-regular graphs with \(\lambda=2\). J. Sib. Fed. Univ. Math. Phys., 2014. Vol. 7, No. 2. P. 204–210.
  3. Behbahani M., Lam C. Strongly regular graphs with nontrivial automorphisms. Discrete Math., 2011. Vol. 311, No. 2–3. P. 132–144. DOI: 10.1016/j.disc.2010.10.005
  4. Cameron P.J. Permutation Groups. London Math. Soc. Student Texts, No. 45. Cambridge: Cambridge Univ. Press, 1999.
  5. Gavrilyuk A.L., Makhnev A.A.} On automorphisms of distance-regular graph with the intersection array \(\{56,45,1;1,9,56\}\). Doklady Mathematics, 2010. Vol. 81, No. 3. P. 439–442. DOI: 10.1134/S1064562410030282
  6. Zavarnitsine A.V. Finite simple groups with narrow prime spectrum. Sib. Electron. Math. Izv., 2009. Vol. 6. P. S1–S12.



DOI: http://dx.doi.org/10.15826/umj.2018.2.008

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