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.

中文翻译：

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通过阻抗块系统的双循环剂

使用图论环境来研究无限性和半规则性之间的联系，这两个概念是在置换组的上下文中自然产生的。除其他外，它表明了一个允许具有两个奇数长度轨道的非平凡自同构的连通弧形传递图，以及一个由正交于这两个轨道的，大小为2的块组成的不定性块系统，是以下两者的规范双覆盖带有两个顶点上的空图\（{\ bar {K}} _ 2 \）的圆弧传递圆弧或圆弧传递圆弧的花环积。