Premium
Doubly transitive 2‐factorizations
Author(s) -
Bonisoli Arrigo,
Buratti Marco,
Mazzuoccolo Giuseppe
Publication year - 2007
Publication title -
journal of combinatorial designs
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.618
H-Index - 34
eISSN - 1520-6610
pISSN - 1063-8539
DOI - 10.1002/jcd.20111
Subject(s) - mathematics , combinatorics , transitive relation , vertex (graph theory) , automorphism group , automorphism , factorization , graph , hypergraph , alternating group , group (periodic table) , discrete mathematics , physics , algorithm , quantum mechanics
Let $\cal F$ be a 2‐factorization of the complete graph K v admitting an automorphism group G acting doubly transitively on the set of vertices. The vertex‐set V ( K v ) can then be identified with the point‐set of AG ( n, p ) and each 2‐factor of $\cal F$ is the union of p ‐cycles which are obtained from a parallel class of lines of AG ( n, p ) in a suitable manner, the group G being a subgroup of A G L ( n, p ) in this case. The proof relies on the classification of 2‐( v, k , 1) designs admitting a doubly transitive automorphism group. The same conclusion holds even if G is only assumed to act doubly homogeneously. © 2006 Wiley Periodicals, Inc. J Combin Designs