Publication detail

Digital Jordan curves and surfaces with respect to a graph connectedness

ŠLAPAL, J.

Czech title

Digitální Jordanovy křivly a plochy vzhledem ke grafové souvislosti.

English title

Digital Jordan curves and surfaces with respect to a graph connectedness

Type

journal article in Web of Science

Language

en

Original 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.

Czech abstract

Zavádíme grafovou souvislost indukovanou danou množinou cest stejné délky. Zaměřujeme se na 2-přilehlý graf na digitální přímce Z s jistou množinou cest délky n pro každé přirozené číslo n. Souvislost v silém součinu dvou, resp. tří kopií tohoto grafu je užita k definici digitální Jordanovy křivky, resp. digitální Jordanovy plochy. Tyto definice jsou založeny na strane-ke-straně dláždění digitální roviny trojúhelníky, resp. stěna-ke-stěně dláždění digitálního (3D) prostoru krychlemi, hranoly a pyramidami.

English 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 in Czech

Jednoduchý graf, silný součin, cesta, souvislost, digitální prostor, Jordanova křivka, Jordanova plocha

Keywords in English

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

Released

08.04.2023

Publisher

Taylor&Francis

Location

Cape Town

ISSN

1727-933X

Volume

46

Number

1

Pages from–to

85–100

Pages count

16

BIBTEX


@article{BUT175987,
  author="Josef {Šlapal},
  title="Digital Jordan curves and surfaces with respect to a graph connectedness",
  year="2023",
  volume="46",
  number="1",
  month="April",
  pages="85--100",
  publisher="Taylor&Francis",
  address="Cape Town",
  issn="1727-933X"
}