On the automorphism groups of almost all circulant graphs and digraphs
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Date
2018
Authors
Bhoumik, Soumya
Dobson, Edward
Morris, Joy
Journal Title
Journal ISSN
Volume Title
Publisher
Drustvo Matematikov, Fizikov in Astronomov
Abstract
We attempt to determine the structure of the automorphism group of a generic circulant graph. We first show that almost all circulant graphs have automorphism groups as small as possible. The second author has conjectured that almost all of the remaining circulant (di)graphs (those whose automorphism group is not as small as possible) are normal circulant (di)graphs. We show this conjecture is not true in general, but is true if we consider only those circulant (di)graphs whose order is in a “large” subset of integers. We note that all non-normal circulant (di)graphs can be classified into two natural classes (generalized wreath products, and deleted wreath type), and show that neither of these classes contains almost every non-normal circulant digraph.
Description
Open access, licensed under Creative Commons
Keywords
Circulant graph , Automorphism group , Caley graph , DRR , GRR , Digraphs
Citation
Bhoumik, S., Dobson, E., & Morris, J. (2014). On the automorphism of almost all circulant graphs and digraphs. Ars Mathematica Contemporanea, 7(2), 487-506