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...

Full description

Saved in:
Bibliographic Details
Published in:Combinatorica (Budapest. 1981) 2018-02, Vol.38 (1), p.1-28
Main Authors: Araújo, João, Bentz, Wolfram, Dobson, Edward, Konieczny, Janusz, Morris, Joy
Format: Article
Language:English
Subjects:
Automorphisms
Combinatorics
Graph theory
Mathematics
Mathematics and Statistics
Monoids
Number theory
Original Paper
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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.
ISSN:0209-9683
1439-6912
DOI:10.1007/s00493-016-3403-0