Publication detail

Walk-set induced connectedness in digital spaces

ŠLAPAL, J.

Original Title

Walk-set induced connectedness in digital spaces

Type

journal article in Web of Science

Language

English

Original Abstract

In an undirected simple graph, we define connectedness induced by a set of walks of the same lengths. We show that the connectedness is preserved by the strong product of graphs with walk sets. This result is used to introduce a graph on the vertex set Z^2 with sets of walks that is obtained as the strong product of a pair of copies of a graph on the vertex set Z with certain walk sets. It is proved that each of the walk sets in the graph introduced induces connectedness on Z^2 that satisfies a digital analogue of the Jordan curve theorem. It follows that the graph with any of the walk sets provides a convenient structure on the digital plane Z^2 for the study of digital images.

Keywords

Simple graph, strong product, walk, connectedness, digital space, Jordan curve theorem

Authors

ŠLAPAL, J.

Released

1. 9. 2017

ISBN

1584-2851

Periodical

Carpathian Journal of Mathematics

Year of study

33

Number

2

State

Romania

Pages from

247

Pages to

256

Pages count

10

URL

http://carpathian.ubm.ro

BibTex

@article{BUT144498,
  author="Josef {Šlapal}",
  title="Walk-set induced connectedness in digital spaces",
  journal="Carpathian Journal of Mathematics",
  year="2017",
  volume="33",
  number="2",
  pages="247--256",
  issn="1584-2851",
  url="http://carpathian.ubm.ro"
}