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arXiv · 2311.08128

Distance-regular Cayley graphs over (pseudo-) semi-dihedral groups

Xueyi Huang·Lu Lu·Xiongfeng Zhan
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Abstract

Distance-regular graphs are a class of regualr graphs with pretty combinatorial symmetry. In 2007, Miklavi\v{c} and Poto\v{c}nik proposed the problem of charaterizing distance-regular Cayley graphs, which can be viewed as a natural extension of the problem of characterizing strongly-regular Cayley graphs (or equivalently, regular partial difference sets). In this paper, we provide a partial characterization for distance-regular Cayley graphs over semi-dihedral groups and pseudo-semi-dihedral groups, both of which are $2$-groups with a cyclic subgroup of index $2$.

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Xueyi Huang, Lu Lu, Xiongfeng Zhan. 2023-11-14. Distance-regular Cayley graphs over (pseudo-) semi-dihedral groups. https://arxiv.org/abs/2311.08128

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