A digital Jordan surface theorem with respect to a graph connectedness

IF 1 4区数学 Q1 MATHEMATICS Open Mathematics Pub Date : 2024-01-06 DOI:10.1515/math-2023-0172

Josef Šlapal

{"title":"A digital Jordan surface theorem with respect to a graph connectedness","authors":"Josef Šlapal","doi":"10.1515/math-2023-0172","DOIUrl":null,"url":null,"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 <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mi mathvariant=\"double-struck\">Z</m:mi> </m:math> {\\mathbb{Z}} with a certain set of paths of length <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mi>n</m:mi> </m:math> n for every positive integer <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mi>n</m:mi> </m:math> 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.","PeriodicalId":48713,"journal":{"name":"Open Mathematics","volume":"54 1","pages":""},"PeriodicalIF":1.0000,"publicationDate":"2024-01-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Open Mathematics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1515/math-2023-0172","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}

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.

查看原文

微信好友朋友圈 QQ好友复制链接

本刊更多论文

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。

求助全文

约1分钟内获得全文去求助

来源期刊

Open Mathematics MATHEMATICS-

CiteScore

2.40

自引率

5.90%

发文量

审稿时长

16 weeks

期刊介绍： Open Mathematics - formerly Central European Journal of Mathematics Open Mathematics is a fully peer-reviewed, open access, electronic journal that publishes significant, original and relevant works in all areas of mathematics. The journal provides the readers with free, instant, and permanent access to all content worldwide; and the authors with extensive promotion of published articles, long-time preservation, language-correction services, no space constraints and immediate publication. Open Mathematics is listed in Thomson Reuters - Current Contents/Physical, Chemical and Earth Sciences. Our standard policy requires each paper to be reviewed by at least two Referees and the peer-review process is single-blind. Aims and Scope The journal aims at presenting high-impact and relevant research on topics across the full span of mathematics. Coverage includes: