After introducing a graph connectedness induced by a given set of paths of the same length, we focus on the 2-adjacency graph on the digital line Z {\mathbb{Z}} with a certain set of paths of length n n for every positive integer n n . The connectedness in the strong product of three copies of the graph is used to define digital Jordan surfaces. These are obtained as polyhedral surfaces bounding the polyhedra that can be face-to-face tiled with digital tetrahedra.

中文翻译：

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关于图连通性的数字乔丹曲面定理

在介绍了由一组给定的相同长度路径引起的图连通性之后，我们重点关注数字线上的 2 邻接图 Z {\mathbb{Z}} 具有一组特定长度的路径 n n 对于每个正整数 n n 。该图的三个副本的强乘积中的连通性用于定义数字约旦曲面。这些是作为包围多面体的多面体表面获得的，可以与数字四面体面对面平铺。