PreprintCC BY 4.0arXiv
On the isomorphism problem of Cayley digraphs
Abstract
A finite group G is called a DCI-group provided any two Cayley digraphs Cay(G,S) and Cay(G,T) are isomorphic iff the two connection sets S and T are images of each other via automorphisms of the group G. Building on the vast literature on CI- and DCI-groups we present an updated list of possible DCI-groups. In addition, we give an alternative proof that does not rely on deep results from group theory. We also point out the three most important open problems related to the classification of DCI-groups.
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BibTeX
@misc{palfy2026isomorphism,
title = {{On the isomorphism problem of Cayley digraphs}},
author = {Péter P. Pálfy},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.33692},
eprint = {2610.33692},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.33692},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - On the isomorphism problem of Cayley digraphs
AU - Péter P. Pálfy
PY - 2026
DA - 2026/10/24
PB - arXiv
DO - 10.48550/arxiv.2610.33692
UR - https://arxiv.org/abs/2610.33692
AB - A finite group G is called a DCI-group provided any two Cayley digraphs Cay(G,S) and Cay(G,T) are isomorphic iff the two connection sets S and T are images of each other via automorphisms of the group G. Building on the vast literature on CI- and DCI-groups we present an updated list of possible DCI-groups. In addition, we give an alternative proof that does not rely on deep results from group theory. We also point out the three most important open problems related to the classification of DCI-groups.
ER -