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On isomorphisms of tetravalent Cayley graphs over generalized quaternion groups
Abstract
Let G be a finite group and S be a subset of G with 1not∈ S. S is called a CI-subset of G if for any T⊂ G, whenever Cay (G,S)≅ Cay (G,T), there is an element σ∈ Aut(G) such that Sσ=T. For a positive integer m, G is called an m-CI-group if all subsets S of G ∖ {1} with |S|≤ m and S−1=S are CI-subsets. In this paper, we show that the generalized quaternion group of order 4n is a $4−CI$-group if and only if n is odd.
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BibTeX
@misc{jin2026isomorphisms,
title = {{On isomorphisms of tetravalent Cayley graphs over generalized quaternion groups}},
author = {Lele Jin and Li Ma and Wei Meng},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.38470},
eprint = {2610.38470},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.38470},
}
RIS
TY - UNPB
TI - On isomorphisms of tetravalent Cayley graphs over generalized quaternion groups
AU - Lele Jin
AU - Li Ma
AU - Wei Meng
PY - 2026
DA - 2026/10/28
PB - arXiv
DO - 10.48550/arxiv.2610.38470
UR - https://arxiv.org/abs/2610.38470
AB - Let G be a finite group and S be a subset of G with 1not∈ S. S is called a CI-subset of G if for any T⊂ G, whenever Cay (G,S)≅ Cay (G,T), there is an element σ∈ Aut(G) such that S^σ=T. For a positive integer m, G is called an m-CI-group if all subsets S of G ∖ {1} with |S|≤ m and S^−1=S are CI-subsets. In this paper, we show that the generalized quaternion group of order 4n is a $4−CI$-group if and only if n is odd.
ER -