One-factorizations of complete graphs with a doubly transitive automorphism group

Peter J. Cameron; Gabor Korchmàros

doi:10.1112/blms/25.1.1

One-factorizations of complete graphs with a doubly transitive automorphism group

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Abstract

It is shown that a 1-factorization of K_n with a doubly transitive automorphism group on vertices is either the affine line-parallelism of AG(d, 2), or one of three ‘sporadic’ examples with n = 6, 12 or 28. The full automorphism groups are respectively AGL (d, 2) (the holomorph of an elementary abelian group of order 2^d), PGL(2, 5), PSL(2, 11) and ΡΓΤ(2, 8).

Original language	English
Pages (from-to)	1-6
Number of pages	6
Journal	Bulletin of the London Mathematical Society
Volume	25
Issue number	1
DOIs	https://doi.org/10.1112/blms/25.1.1
Publication status	Published - 1 Jan 1993

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AB - It is shown that a 1-factorization of Kn with a doubly transitive automorphism group on vertices is either the affine line-parallelism of AG(d, 2), or one of three ‘sporadic’ examples with n = 6, 12 or 28. The full automorphism groups are respectively AGL (d, 2) (the holomorph of an elementary abelian group of order 2d), PGL(2, 5), PSL(2, 11) and ΡΓΤ(2, 8).

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One-factorizations of complete graphs with a doubly transitive automorphism group

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