非标准有向图
Nonstandard Digraphs
摘要：
非标准图已被定义和检查在以前的作品。本文对非标准有向图也做了同样的工作。由于有向图比图有更多的结构，所以本文的讨论需要更复杂的定义，并产生了非标准有向图所特有的各种结果。一个非标准有向图可以通过一个基于有向图序列的超幂构造得到，或者更巧妙地利用转移原理得到。我们在特定情况下使用其中一种或两种技术。作为特殊情况，我们有一个单一的无限有向图和超有限有向图序列的基础上扩大。还审查了这样的想法，作为非标准弧和顶点，连通性，组件和星系的非标准有向图的发病率和邻接。
英文摘要：
Nonstandard graphs have been defined and examined in prior works. The present work does the same for nonstandard digraphs. Since digraphs have more structure than do graphs, the present discussion requires more complicated definitions and yields a variety of results peculiar to nonstandard digraphs. A nonstandard digraph can be obtained by means of an ultrapower construction based on a sequence of digraphs or more elegantly by using the transfer principle. We use either or both techniques in particular circumstances. As special cases, we have the enlargement of a single infinite digraph and also hyperfinite digraphs based on sequences of finite digraphs. Also examined are such ideas as incidences and adjacencies for nonstandard arcs and vertices, connectedness, components, and galaxies in nonstandard digraphs.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
