Mixed graphs can be seen as digraphs that have both arcs and edges (or digons, that is, two opposite arcs). In this paper, we consider the case where such graphs are Cayley graphs of abelian groups. Such groups can be constructed using a generalization to \(\mathbb {Z}^n\) of the concept of congruence in \(\mathbb {Z}\). Here we use this approach to present some families of mixed graphs, which, for every fixed value of the degree, have an asymptotically large number of vertices as the diameter increases. In some cases, the results obtained are shown to be optimal.

中文翻译：

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新的摩尔定界和Abelian Cayley混合图的一些最佳族

混合图可以看作是既有弧又有边（或对角线，即两个相对的弧）的有向图。在本文中，我们考虑这种图是阿贝尔群的Cayley图的情况。这样的基团可以使用一般化要构造\（\ mathbb {Z} ^ N \）在同余的概念\（\ mathbb {Z} \） 。在这里，我们使用这种方法来呈现一些混合图族，对于度的每个固定值，随着直径的增加，它们具有渐近大量的顶点。在某些情况下，获得的结果显示为最佳。