Publication Details

Path-induced closure operators on graphs for defining digital Jordan surfaces

ŠLAPAL, J. Path-induced closure operators on graphs for defining digital Jordan surfaces. Open Mathematics, 2019, vol. 17, no. 1, p. 1374-1380. ISSN: 2391-5455.
Czech title
Uzávěrové operátory na grafech indukované cestami pro definování digitálních Jordanových ploch
Type
journal article
Language
English
Authors
Šlapal Josef, prof. RNDr., CSc. (IM DAAG)
URL
Keywords

simple graph, path, closure operator, connectedness, digital space, digital surface, Khalimsky topology, Jordan surface theorem

Abstract

Given a simple graph with the vertex set X, we discuss a closure operator on X induced by a set of paths with identical lengths in the graph. We introduce a certain set of paths of the same length in the 2-adjacency graph on the digital line Z and consider the closure operators on Z^m (m a positive integer) that are induced by a special product of m copies of the introduced set of paths. We focus on the case m = 3 and show that the closure operator considered provides the digital space Z^3 with a connectedness that may be used for defining digital surfaces satisfying a Jordan surface theorem.

Published
2019
Pages
1374–1380
Journal
Open Mathematics, vol. 17, no. 1, ISSN 2391-5455
DOI
10.1515/math-2019-0121
UT WoS
000501136200003
EID Scopus
2-s2.0-85076277698
BibTeX 
@article{BUT162077,
  author="Josef {Šlapal}",
  title="Path-induced closure operators on graphs for defining digital Jordan surfaces",
  journal="Open Mathematics",
  year="2019",
  volume="17",
  number="1",
  pages="1374--1380",
  doi="10.1515/math-2019-0121",
  issn="2391-5455",
  url="https://www.degruyter.com/view/j/math.2019.17.issue-1/math-2019-0121/math-2019-0121.xml?format=INT"
}
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