Journal article

ŠLAPAL Josef. Closure operators on graphs for modeling connectedness in digital spaces. FILOMAT. Niš: University of Niš, 2018, vol. 2018, no. 14, pp. 5011-5021. ISSN 0354-5180. Available from: http://journal.pmf.ni.ac.rs/filomat/index.php/filomat/article/view/7904
Publication language:english
Original title:Closure operators on graphs for modeling connectedness in digital spaces
Title (cs):Uzávěrové operátory na grafech pro modelování souvislosti v digitálních prostorech
Pages:5011-5021
Place:RS
Year:2018
URL:http://journal.pmf.ni.ac.rs/filomat/index.php/filomat/article/view/7904
Journal:FILOMAT, Vol. 2018, No. 14, Niš, RS
ISSN:0354-5180
DOI:10.2298/FIL1814011S
Keywords
Simple grap, walk, closure operator, digital space, Khalimsky topology, Jordan curve theorem
Annotation
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.
BibTeX:
@ARTICLE{
   author = {Josef {\v{S}}lapal},
   title = {Closure operators on graphs for modeling
	connectedness in digital spaces},
   pages = {5011--5021},
   journal = {FILOMAT},
   volume = {2018},
   number = {14},
   year = {2018},
   ISSN = {0354-5180},
   doi = {10.2298/FIL1814011S},
   language = {english},
   url = {http://www.fit.vutbr.cz/research/view_pub.php?id=11938}
}

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