Publication Details

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

ŠLAPAL, J. Categorical aspects of inducing closure operators on graphs by sets of walks. JOURNAL OF COMPUTER AND SYSTEM SCIENCES, 2018, vol. 2018, no. 95, p. 143-150. ISSN: 0022-0000.
Czech title
Kategoriální aspekty indukování uzávěrových operátorů na grafech množinami cest
Type
journal article
Language
English
Authors
Šlapal Josef, prof. RNDr., CSc. (IM DAAG)
URL
Keywords

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

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.

Published
2018
Pages
143–150
Journal
JOURNAL OF COMPUTER AND SYSTEM SCIENCES, vol. 2018, no. 95, ISSN 0022-0000
DOI
10.1016/j.jcss.2017.02.005
UT WoS
000431386900012
EID Scopus
2-s2.0-85019704726
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"
}
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