从扩充有向图到电压有向图和线图的提升
From expanded digraphs to lifts of voltage digraphs and line digraphs
摘要：
本文提出了一种由小有向图构造大有向图的一般方法。这些被称为扩展的有向图，并作为特殊情况下，我们展示了提升的有向图的电压有向图和线有向图，这是两个已知的方法来获得密集的有向图之间的密切关系。在相同的上下文中，我们证明了顶点分裂和部分线有向图技术之间的等价性。然后，我们给出了基线图的提升图仍是线图的一个充分条件。一些结果说明了两个著名的家庭的有向图。也就是说，德Bruijn和Kautz有向图，它表明，这两个家庭可以被视为电梯较小的德Bruijn有向图与适当的电压分配。
英文摘要：
In this note we present a general approach to construct large digraphs from small ones. These are called expanded digraphs, and, as particular cases, we show the close relationship between lifted digraphs of voltage digraphs and line digraphs, which are two known ways to obtain dense digraphs. In the same context, we show the equivalence between the vertex-splitting and partial line digraph techniques. Then, we give a sufficient condition for a lifted digraph of a base line digraph to be again a line digraph. Some of the results are illustrated with two well-known families of digraphs. Namely, the De Bruijn and Kautz digraphs, where it is shown that both families can be seen as lifts of smaller De Bruijn digraphs with appropriate voltage assignments.
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