Normal Cayley digraphs of cyclic groups with CI-property

A Cayley (di)graph of a group G is called normal if the right regular representation of G is normal in the full automorphism group of and a CI-(di)graph if for every Cayley (di)graph implies that there is such that We call a group G an NDCI-group or NCI-group if all normal Cayley digraphs or graphs...

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Bibliographic Details
Published in:Communications in algebra 2022-07, Vol.50 (7), p.2911-2920
Main Authors: Xie, Jin-Hua, Feng, Yan-Quan, Ryabov, Grigory, Liu, Ying-Long
Format: Article
Language:English
Subjects:
Automorphisms
Cayley digraph
CI-group
DCI-group
Graph theory
Graphs
NCI-group
NDCI-group
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Summary:A Cayley (di)graph of a group G is called normal if the right regular representation of G is normal in the full automorphism group of and a CI-(di)graph if for every Cayley (di)graph implies that there is such that We call a group G an NDCI-group or NCI-group if all normal Cayley digraphs or graphs of G are CI-digraphs or CI-graphs, respectively. We prove that a cyclic group of order n is an NDCI-group if and only if and an NCI-group if and only if either n = 8 or
ISSN:0092-7872
1532-4125
DOI:10.1080/00927872.2021.2022156