Result Details

Digital Jordan curves and surfaces with respect to a graph connectedness

ŠLAPAL, J. Digital Jordan curves and surfaces with respect to a graph connectedness. Quaestiones Mathematicae, 2023, vol. 46, no. 1, p. 85-100. ISSN: 1727-933X.
Type
journal article
Language
English
Authors
Šlapal Josef, prof. RNDr., CSc., IM DAAG (FME)
Abstract

We introduce a graph connectedness induced by a given set of paths
of the same length. We focus on the 2-adjacency graph on the digital line Z with
a certain set of paths of length n for every positive integer n. The connectedness
in the strong product of two and three copies of the graph is used to define digital
Jordan curves and digital Jordan surfaces, respectively. Such definitions build on
an edge-to-edge tiling with triangles in the digital plane and a face-to-face tiling by
cubes, prisms and pyramids in the (3D) digital space, respectively.

Keywords

Simple graph, strong product, path, connectedness, digital space, Jordan
curve, Jordan surface

URL
Published
2023
Pages
85–100
Journal
Quaestiones Mathematicae, vol. 46, no. 1, ISSN 1727-933X
Publisher
Taylor&Francis
Place
Cape Town
DOI
10.2989/16073606.2021.2011466
UT WoS
000742468700001
EID Scopus
2-s2.0-85122866265
BibTeX 
@article{BUT175987,
  author="Josef {Šlapal}",
  title="Digital Jordan  curves and surfaces with respect to a graph connectedness",
  journal="Quaestiones Mathematicae",
  year="2023",
  volume="46",
  number="1",
  pages="85--100",
  doi="10.2989/16073606.2021.2011466",
  issn="1607-3606",
  url="https://www.tandfonline.com/eprint/YCG5ADY3K2UQGMSA7UGR/full?target=10.2989/16073606.2021.2011466"
}
Departments
Institute of Mathematics (IM)
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