Detail publikačního výsledku

Categorical aspects of inducing closure operators on graphs by sets of walks

ŠLAPAL, J.

Originální název

Categorical aspects of inducing closure operators on graphs by sets of walks

Anglický název

Categorical aspects of inducing closure operators on graphs by sets of walks

Druh

Článek WoS

Originální abstrakt

We study closure operators on graphs which are induced by sets of walks of identical lengths in these graphs. It is shown that the induction gives rise to a Galois correspondence between the category of closure spaces and that of graphs with walk sets. We study the two isomorphic subcategories resulting from the correspondence, in particular, the one that is a full subcategory of the category of graphs with walk sets. As examples, we discuss closure operators that are induced by path sets on some natural graphs on the digital plane Z2. These closure operators are shown to include the well known Marcus-Wyse and Khalimsky topologies, thus indicating the possibility of using them as convenient background structures on the digital plane for the study of geometric and topological properties of digital images.

Anglický abstrakt

We study closure operators on graphs which are induced by sets of walks of identical lengths in these graphs. It is shown that the induction gives rise to a Galois correspondence between the category of closure spaces and that of graphs with walk sets. We study the two isomorphic subcategories resulting from the correspondence, in particular, the one that is a full subcategory of the category of graphs with walk sets. As examples, we discuss closure operators that are induced by path sets on some natural graphs on the digital plane Z2. These closure operators are shown to include the well known Marcus-Wyse and Khalimsky topologies, thus indicating the possibility of using them as convenient background structures on the digital plane for the study of geometric and topological properties of digital images.

Klíčová slova

Simple graph, Path, Closure operator, Galois correspondence, Diagonal set of paths, Digital topology

Klíčová slova v angličtině

Simple graph, Path, Closure operator, Galois correspondence, Diagonal set of paths, Digital topology

Autoři

ŠLAPAL, J.

Rok RIV

2019

Vydáno

08.06.2018

ISSN

0022-0000

Periodikum

JOURNAL OF COMPUTER AND SYSTEM SCIENCES

Svazek

2018

Číslo

95

Stát

Spojené státy americké

Strany od

143

Strany do

150

Strany počet

8

URL

https://www.sciencedirect.com/science/article/pii/S0022000017300247?via%3Dihub

BibTex

@article{BUT131358,
  author="Josef {Šlapal}",
  title="Categorical aspects of inducing closure operators on graphs by sets of walks",
  journal="JOURNAL OF COMPUTER AND SYSTEM SCIENCES",
  year="2018",
  volume="2018",
  number="95",
  pages="143--150",
  doi="10.1016/j.jcss.2017.02.005",
  issn="0022-0000",
  url="https://www.sciencedirect.com/science/article/pii/S0022000017300247?via%3Dihub"
}

Dokumenty

JCSS2018