Publication Details

Closure operators on graphs for modeling connectedness in digital spaces

ŠLAPAL, J. Closure operators on graphs for modeling connectedness in digital spaces. FILOMAT, 2018, vol. 32, no. 14, p. 5011-5021. ISSN: 0354-5180.
Czech title
Uzávěrové operátory na grafech pro modelování souvislosti v digitálních prostorech
Type
journal article
Language
English
Authors
Šlapal Josef, prof. RNDr., CSc. (IM DAAG)
URL
Keywords

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

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.

Published
2018
Pages
5011–5021
Journal
FILOMAT, vol. 32, no. 14, ISSN 0354-5180
DOI
10.2298/FIL1814011S
UT WoS
000461183400018
EID Scopus
2-s2.0-85060868606
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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