Publication detail

Galois connections between sets of paths and closure operators in simple graphs

ŠLAPAL, J.

Original Title

Galois connections between sets of paths and closure operators in simple graphs

Type

journal article in Web of Science

Language

English

Original Abstract

For every positive integer n,we introduce and discuss an isotone Galois connection between the sets of paths of lengths n in a simple graph and the closure operators on the (vertex set of the) graph.We consider certain sets of paths in a particular graph on the digital line Z and study the closure operators associated, in the Galois connection discussed, with these sets of paths. We also focus on the closure operators on the digital plane Z^2 associated with a special product of the sets of paths considered and show that these closure operators may be used as background structures on the plane for the study of digital images.

Keywords

Simple graph, Closure operator, Galois connection, digital space, Khalimsky topology, Jordan curve theorem.

Authors

ŠLAPAL, J.

Released

31. 12. 2018

ISBN

2391-5455

Periodical

Open Mathematics

Year of study

16

Number

1

State

Republic of Poland

Pages from

1573

Pages to

1581

Pages count

9

URL

https://www.degruyter.com/downloadpdf/j/math.2018.16.issue-1/math-2018-0128/math-2018-0128.pdf

BibTex

@article{BUT155612,
  author="Josef {Šlapal}",
  title="Galois connections between sets of paths and closure operators in simple graphs",
  journal="Open Mathematics",
  year="2018",
  volume="16",
  number="1",
  pages="1573--1581",
  doi="10.1515/math-2018-0128",
  issn="2391-5455",
  url="https://www.degruyter.com/downloadpdf/j/math.2018.16.issue-1/math-2018-0128/math-2018-0128.pdf"
}