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On automorphisms of strongly regular graphs with parameters λ = 1, μ = 2
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A. A. Makhnev
Published/Copyright:
June 1, 2004
Let Γ be a strongly regular graph with parameters (v, k, 1, 2). Then k = u2 + u + 2 and u = 1, 3, 4, 10, or 31. It is known that such graphs exist for u equal to 1 and 4. They are the (3 × 3)-lattice and the graph of cosets of the ternary Golay code. If u = 3, then Γ has the parameters (99, 14, 1, 2). The question on existence of such graphs was posed by J. Seidel.
With the use of theory of characters of finite groups we find the possible orders and the structures of subgraphs of the fixed points of automorphisms of the graph Γ with parameters (99, 14, 1, 2). It is proved that if the group Aut(Γ) contains an involution, then its order divides 42.
Published Online: 2004-06-01
Published in Print: 2004-06-01
Copyright 2004, Walter de Gruyter
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Articles in the same Issue
- Vladimir Yakovlevich Kozlov (to the ninetieth anniversary)
- Hopf algebras of linear recurring sequences
- Necessary conditions for solvability of a system of linear equations over a ring
- Loop codes
- On the complexity of realisation of Zhegalkin polynomials
- On new classes of conjugate injectors of finite groups
- On automorphisms of strongly regular graphs with parameters λ = 1, μ = 2
- On large deviations for the Shepp statistic
Articles in the same Issue
- Vladimir Yakovlevich Kozlov (to the ninetieth anniversary)
- Hopf algebras of linear recurring sequences
- Necessary conditions for solvability of a system of linear equations over a ring
- Loop codes
- On the complexity of realisation of Zhegalkin polynomials
- On new classes of conjugate injectors of finite groups
- On automorphisms of strongly regular graphs with parameters λ = 1, μ = 2
- On large deviations for the Shepp statistic
