Automorphism Groups of Circulant Digraphs with Applications to Semigroup Theory Araújo, João; Bentz, Wolfram; Edward Dobson; Janusz Konieczny; Joy Morris

Submitted

We characterize the automorphism groups of circulant digraphs whose connection
sets are relatively small, and of unit circulant digraphs. For each class, we either
explicitly determine the automorphism group or we show that the graph is \normal"
circulant, so the automorphism group is contained in the normalizer of a cycle. Then we
use these characterizations to prove results on the automorphisms of the endomorphism
monoids of those digraphs. The paper ends with a list of open problems on graphs,
number theory, groups and semigroups.