A graph G is called pancyclic if it contains a cycle of length l for each integer l from 3 to |V (G)| inclusive, where |V (G)| denotes the cardinality of the vertex set of graph G. It has been shown by Ma et al. (2007) that the augmented cube, proposed by Choudum and Sunitha (2002), is pancyclic. In this paper, we propose a more refined property, namely double-pancyclicity. Let G be a pancyclic graph with N vertices, and (u1, v1), (u2, v2) be any two vertex-disjoint edges in G. Moreover, let l1 and l2 be any two integers of {3, 4, …, N − 3} such that l1 + l2 ≤ N. Then G is said to be double-pancyclic if it has two vertexdisjoint cycles, C1 and C2, such that |V (Ci)| = li and (ui, vi) ∈ E(Ci) for i = 1, 2. Moreover, we show that the class of augmented cubes can be almost double-pancyclic.
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机译：如果它包含每个整数L的长度L的循环，则称为Pancyclic，从3到| V（g）|包容性，其中| V（g）|表示图表G的顶点组的基数。它已被Ma等人显示。 （2007）Choudum和Sunitha（2002）提出的增强立方体是北京的。在本文中，我们提出了更加精致的财产，即双重羽毛性。设g是一个具有n顶点的挂钩图，（U 1 ，V 1 ），（U 2 ，V 2 < / inf>）是G的任何两个顶点不相交的边缘。此外，让L 1 和L 2 是{3,4，...，n的任何两个整数 - 3}这样L 1 + L 2 ≤N。然后，如果它有两个顶端Clyclic，则G. C 1 和C 2 ，这样| V（C I ）| = L I 和（U I ，V I ）对于i = 1，此外，我们表明增强立方体的类别几乎是双重羽毛的。
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