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Automorphism groups of circulant digraphs with applications to semigroup theory

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

Authors

João Araújo

Wolfram Bentz

Edward Dobson

Janusz Konieczny

Joy Morris



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
Electronic ISSN 1439-6912
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
Copyright Statement ©2018 University of Hull
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

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