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Publication detail
ŠLAPAL, J.
Original Title
Closure operators on graphs for modeling connectedness in digital spaces
Type
journal article in Web of Science
Language
English
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.
Keywords
Simple grap, walk, closure operator, digital space, Khalimsky topology, Jordan curve theorem
Authors
Released
26. 11. 2018
ISBN
0354-5180
Periodical
FILOMAT
Year of study
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" }