Automorphism groups of circulant digraphs with applications to semigroup theory

Araújo, João; Bentz, Wolfram; Dobson, Edward; Konieczny, Janusz; Morris, Joy

Abstract

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 a "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.

Citation

Araújo, J., Bentz, W., Dobson, E., Konieczny, J., & Morris, J. (2018). Automorphism groups of circulant digraphs with applications to semigroup theory. Combinatorica, 38(1), 1-28. https://doi.org/10.1007/s00493-016-3403-0

• Acceptance Date: Dec 12, 2015
• Online Publication Date: Feb 13, 2017
• Publication Date: 2018-02
• Deposit Date: Mar 9, 2016
• Publicly Available Date: Feb 14, 2018
• Journal: Combinatorica
• Print ISSN: 0209-9683
• Publisher: Springer Verlag
• Peer Reviewed: Peer Reviewed
• Volume: 38
• Issue: 1
• Pages: 1-28
• DOI: https://doi.org/10.1007/s00493-016-3403-0
• Keywords: Circulant digraphs; Automorphisms
• Public URL: https://hull-repository.worktribe.com/output/412492
• Publisher URL: http://link.springer.com/article/10.1007%2Fs00493-016-3403-0
• Additional Information: Authors' accepted manuscript of article published in: Combinatorica, 2017. The final publication is available at Springer via http://dx.doi.org/10.1007/s00493-016-3403-0
• Contract Date: Feb 14, 2018