Publication Details

Walk-set induced connectedness in digital spaces

ŠLAPAL Josef. Walk-set induced connectedness in digital spaces. Carpathian Journal of Mathematics, vol. 33, no. 2, 2017, pp. 247-256. ISSN 1584-2851. Available from: http://carpathian.ubm.ro
Czech title
Souvislost v digitálním prostoru indukovaná množinami cest
Type
journal article
Language
english
Authors
Šlapal Josef, prof. RNDr., CSc. (RCIT FIT BUT)
URL
Keywords

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

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.

Published
2017
Pages
247-256
Journal
Carpathian Journal of Mathematics, vol. 33, no. 2, ISSN 1584-2851
Publisher
Dpt. of Math. and Comp. Sci., Technical Univ. of Cluj-Napoca
UT WoS
000411780600011
EID Scopus
BibTeX
@ARTICLE{FITPUB11589,
   author = "Josef \v{S}lapal",
   title = "Walk-set induced connectedness in digital spaces",
   pages = "247--256",
   journal = "Carpathian Journal of Mathematics",
   volume = 33,
   number = 2,
   year = 2017,
   ISSN = "1584-2851",
   language = "english",
   url = "https://www.fit.vut.cz/research/publication/11589"
}
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