On the automorphism groups of almost all circulant graphs and digraphs
Drustvo Matematikov, Fizikov in Astronomov
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.
Open access, licensed under Creative Commons
Circulant graph , Automorphism group , Caley graph , DRR , GRR , Digraphs
Bhoumik, S., Dobson, E., & Morris, J. (2014). On the automorphism of almost all circulant graphs and digraphs. Ars Mathematica Contemporanea, 7(2), 487-506