Normal Cayley digraphs of generalized quaternion groups with CI-property

Jin-Hua Xie, Yan-Quan Feng and Young Soo Kwon

Applied Mathematics and Computation, 2022, vol. 422, issue C

Abstract: A Cayley digraph Cay(G,S) of a finite group G with respect to a subset S of G, where S does not contain the identity 1 of G, is said to be a CI-digraph, if Cay(G,S)≅Cay(G,T) implies that G has an automorphism mapping S to T. The group G is called a DCI-group or an NDCI-group if all Cayley digraphs or normal Cayley digraphs of G are CI-digraphs. We prove in this paper that a generalized quaternion group Q4n of order 4n is an NDCI-group if and only if n=2 or n is odd. As a result, we show that if Q4n is a DCI-group then n=2 or n is odd-square-free.

Keywords: CI-Digraph; NDCI-Group; DCI-Group; Generalized quaternion group (search for similar items in EconPapers)
Date: 2022
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:422:y:2022:i:c:s0096300322000522

DOI: 10.1016/j.amc.2022.126966

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