Asymptotic Automorphism Groups of Circulant Graphs and Digraphs

Details Asymptotic Automorphism Groups of Circulant Graphs and Digraphs Asymptotic Automorphism Groups of Circulant Graphs and Digraphs

2012-03-04

arxiv.org/abs/1203.0707v1

Mathematics

Combinatorics

26 pages

Scientific paper

We show that almost all circulant graphs have automorphism groups as small as possible. Of the circulant graphs that do not have automorphism group as small as possible, we give some families of integers such that it is not true that almost all circulant graphs whose order lies in any one of these families, are normal. That almost all Cayley (di)graphs whose automorphism group is not as small as possible are normal was conjectured by the second author, so these results provide counterexamples to this conjecture. It is then shown that there is a large family of integers for which almost every circulant digraph whose order lies in this family and that does not have automorphism group as small as possible, is normal. We additionally explore the asymptotic behavior of the automorphism groups of circulant (di)graphs that are not normal, and show that no general conclusion can be obtained.

Affiliated with

Also associated with

No associations

Rating

Asymptotic Automorphism Groups of Circulant Graphs and Digraphs does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Asymptotic Automorphism Groups of Circulant Graphs and Digraphs, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Asymptotic Automorphism Groups of Circulant Graphs and Digraphs will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-331434