Publication result detail

Closure operators on graphs for modeling connectedness in digital spaces

ŠLAPAL, J.

Original Title

Closure operators on graphs for modeling connectedness in digital spaces

English Title

Closure operators on graphs for modeling connectedness in digital spaces

Type

WoS Article

Original Abstract

For undirected simple graphs, we introduce closure operators on their vertex sets induced by sets of walks of the same lengths. Some basic properties of these closure operators are studied, with greater attention paid to connectedness. We focus on the closure operators induced by certain sets of walks in the 2-adjacency graph on the digital line Z, which generalize the Khalimsky topology. For the closure operators on Z^2 obtained as particularly defined products of pairs of the induced closure operators on Z, we formulate and prove a digital form of the Jordan curve theorem.

English abstract

For undirected simple graphs, we introduce closure operators on their vertex sets induced by sets of walks of the same lengths. Some basic properties of these closure operators are studied, with greater attention paid to connectedness. We focus on the closure operators induced by certain sets of walks in the 2-adjacency graph on the digital line Z, which generalize the Khalimsky topology. For the closure operators on Z^2 obtained as particularly defined products of pairs of the induced closure operators on Z, we formulate and prove a digital form of the Jordan curve theorem.

Keywords

Simple grap, walk, closure operator, digital space, Khalimsky topology, Jordan curve theorem

Key words in English

Simple grap, walk, closure operator, digital space, Khalimsky topology, Jordan curve theorem

Authors

ŠLAPAL, J.

RIV year

2019

Released

26.11.2018

ISBN

0354-5180

Periodical

Filomat

Volume

32

Number

14

State

Republic of Serbia

Pages from

5011

Pages to

5021

Pages count

11

URL

http://journal.pmf.ni.ac.rs/filomat/index.php/filomat/article/view/7904

BibTex

@article{BUT155935,
  author="Josef {Šlapal}",
  title="Closure operators on graphs for modeling connectedness in digital spaces",
  journal="Filomat",
  year="2018",
  volume="32",
  number="14",
  pages="5011--5021",
  doi="10.2298/FIL1814011S",
  issn="0354-5180",
  url="http://journal.pmf.ni.ac.rs/filomat/index.php/filomat/article/view/7904"
}

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