A digital Jordan surface theorem with respect to a graph connectedness

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-01-06 DOI:10.1515/math-2023-0172

Josef Šlapal

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引用次数: 0

Abstract

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

{\mathbb{Z}}

with a certain set of paths of length

for every positive integer

. 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.

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关于图形连通性的数字乔丹曲面定理

在介绍了由一组长度相同的给定路径所诱导的图连通性之后，我们将重点放在数字线 Z {\mathbb{Z}} 上的 2-相接图上，对于每一个正整数 n n，该图具有一组长度为 n n 的路径。图的三个副本的强积中的连通性被用来定义数字乔丹曲面。这些曲面作为多面体的边界，可以与数字四面体面对面平铺。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.