Publication detail

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

ŠLAPAL, J.

Original Title

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

Type

journal article in Web of Science

Language

English

Original Abstract

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.

Keywords

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

Authors

ŠLAPAL, J.

Released

8. 6. 2018

ISBN

0022-0000

Periodical

JOURNAL OF COMPUTER AND SYSTEM SCIENCES

Year of study

2018

Number

95

State

United States of America

Pages from

143

Pages to

150

Pages count

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"
}