Publication result 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

English Title

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

Type

WoS Article

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.

English 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

Key words in English

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

Authors

ŠLAPAL, J.

RIV year

2020

Released

19.11.2019

ISBN

2391-5455

Periodical

Open Mathematics

Volume

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

open-mathematics-slapal2019
OpenMath2019