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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

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.

Publication Date 2018-02
Journal Combinatorica
Print ISSN 0209-9683
Electronic ISSN 1439-6912
Publisher Springer Verlag
Peer Reviewed Peer Reviewed
Volume 38
Issue 1
Pages 1-28
Institution 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
DOI https://doi.org/10.1007/s00493-016-3403-0
Keywords Circulant digraphs; Automorphisms
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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