Paper Info
Title
Automorphisms and Enumeration of Switching Classes of Tournaments
Abstract
Two tournaments T1 and T2 on the same vertex set X are said to be switching equivalent if X has a subset Y such that T2 arises from T1 by switching all arcs between Y and its complement XnY . The main result of this paper is a characterisation of the abstract nite groups which are full automorphism groups of switching classes of tournaments: they are those whose Sylow 2-subgroups are cyclic or dihedral. Moreover, if G is such a group, then there is a switching class C ,w ith Aut(C) = G, such that every subgroup ofG of odd order is the full automorphism group of some tournament in C. Unlike previous results of this type, we do not give an explicit con- struction, but only an existence proof. The proof follows as a special case of a result on the full automorphism group of randomG-invariant digraphs selected from a certain class of probability distributions. We also show that a permutation group G, acting on a set X ,i s contained in the automorphism group of some switching class of tour- naments with vertex set X if and only if the Sylow 2-subgroups of
Year
Venue
Keywords
2000
Electr. J. Comb.
permutation group,probability distribution
Field
DocType
Volume
Outer automorphism group,Discrete mathematics,Combinatorics,Sylow theorems,Symmetric group,Automorphism,p-group,Permutation group,Inner automorphism,Mathematics,Alternating group
Journal
7
Citations 
PageRank 
References 
5
1.11
2
Authors
2
Name
Order
Citations
PageRank
Laszlo Babai13537573.58
Peter J. Cameron2450121.91