Abstract
A graph-theoretic environment is used to study the connection between imprimitivity and semiregularity, two concepts arising naturally in the context of permutation groups. Among other, it is shown that a connected arc-transitive graph admitting a nontrivial automorphism with two orbits of odd length, together with an imprimitivity block system consisting of blocks of size 2, orthogonal to these two orbits, is either the canonical double cover of an arc-transitive circulant or the wreath product of an arc-transitive circulant with the empty graph \({\bar{K}}_2\) on two vertices.
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The author wishes to thank Ademir Hujdurović and Klavdija Kutnar for helpful conversations about the material of this paper.
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This work is supported in part by the Slovenian Research Agency (I0-0035, research program P1-0285 and research projects N1-0062, J1-9108, J1-1695, N1-0140 and J1-2451)
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Marušič, D. Bicirculants via Imprimitivity Block Systems. Mediterr. J. Math. 18, 116 (2021). https://doi.org/10.1007/s00009-021-01771-z
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DOI: https://doi.org/10.1007/s00009-021-01771-z