Automorphism Groups of Circulant Digraphs With Applications to Semigroup Theory

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...

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Veröffentlicht in:	Combinatorica (Budapest. 1981) 2018-02, Vol.38 (1), p.1-28
Hauptverfasser:	Araújo, João, Bentz, Wolfram, Dobson, Edward, Konieczny, Janusz, Morris, Joy
Format:	Artikel
Sprache:	eng
Schlagworte:	Automorphisms Combinatorics Graph theory Mathematics Mathematics and Statistics Monoids Number theory Original Paper
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container_title	Combinatorica (Budapest. 1981)
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creator	Araújo, João Bentz, Wolfram Dobson, Edward Konieczny, Janusz Morris, Joy
description	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.
doi_str_mv	10.1007/s00493-016-3403-0
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subjects	Automorphisms Combinatorics Graph theory Mathematics Mathematics and Statistics Monoids Number theory Original Paper
title	Automorphism Groups of Circulant Digraphs With Applications to Semigroup Theory
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