Abstract A Cayley graph Γ \Gamma on a group G is called a dual Cayley graph on G if the left regular representation of G is a subgroup of the automorphism group of Γ \Gamma (note that the right regular representation of G is always an automorphism group of Γ \Gamma ). In this article, we study finite dual Cayley graphs regarding identification, construction, transitivity and such graphs with automorphism groups as small as possible. A few problems worth further research are also proposed.

中文翻译：

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在有限对偶凯莱图上

摘要 如果 G 的左正则表示是 Γ \Gamma 的自同构群的子群，则 G 上的凯莱图 Γ \Gamma 称为 G 上的对偶凯莱图（注意 G 的右正则表示总是自同构Γ \Gamma ) 的群。在本文中，我们研究了关于识别、构造、传递性的有限对偶 Cayley 图以及此类具有尽可能小的自同构群的图。还提出了一些值得进一步研究的问题。