Publication detail

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

ŠLAPAL, J.

Original Title

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

Type

journal article in Web of Science

Language

English

Original 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.

Keywords

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

Authors

ŠLAPAL, J.

Released

19. 11. 2019

ISBN

2391-5455

Periodical

Open Mathematics

Year of study

17

Number

1

State

Republic of Poland

Pages from

1374

Pages to

1380

Pages count

7

URL

https://www.degruyter.com/view/j/math.2019.17.issue-1/math-2019-0121/math-2019-0121.xml?format=INT

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"
}

Documents

OpenMath2019.pdf