Vertex-primitive self-complementary graphs were proved to be affine or in product action by Guralnick et al. [‘On orbital partitions and exceptionality of primitive permutation groups’, Trans. Amer. Math. Soc.356 (2004), 4857–4872]. The product action type is known in some sense. In this paper, we provide a generic construction for the affine case and several families of new self-complementary Cayley graphs are constructed.

中文翻译：

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自互补凯利图的新结构

Guralnick 证明顶点原始自互补图是仿射的或在乘积作用中等。['关于原始置换群的轨道划分和例外性'，反式。阿米尔。数学。社会党。356(2004), 4857–4872]。产品操作类型在某种意义上是已知的。在本文中，我们为仿射情况提供了一个通用构造，并构造了几个新的自互补凯莱图族。