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One‐factorizations of complete graphs with vertex‐regular automorphism groups
Author(s) -
Bonisoli Arrigo,
Labbate Domenico
Publication year - 2001
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.1025
Subject(s) - mathematics , dihedral group , combinatorics , vertex (graph theory) , abelian group , dihedral angle , automorphism group , automorphism , upper and lower bounds , group (periodic table) , p group , discrete mathematics , graph , mathematical analysis , hydrogen bond , chemistry , organic chemistry , molecule
We consider one‐factorizations of K 2 n possessing an automorphism group acting regularly (sharply transitively) on vertices. We present some upper bounds on the number of one‐factors which are fixed by the group; further information is obtained when equality holds in these bounds. The case where the group is dihedral is studied in some detail, with some non‐existence statements in case the number of fixed one‐factors is as large as possible. Constructions both for dihedral groups and for some classes of abelian groups are given. © 2002 John Wiley & Sons, Inc. J Combin Designs 10: 1–16, 2002