Publication Details

Terse walk sets in graphs and induced closure operators

ŠLAPAL, J. Terse walk sets in graphs and induced closure operators. Topology and its Applications, 2017, vol. 230, no. 1, p. 258-266. ISSN: 0166-8641.
Czech title
Střízlivé množiny sledů v grafech a indukované uzávěrové operátory
Type
journal article
Language
English
Authors
Šlapal Josef, prof. RNDr., CSc. (IM DAAG)
Keywords

Simple graph, alpha-walk, terse walk set, closure operator, direct limit

Abstract

Given a graph G, for every ordinal a > 1, we introduce and study closure operators on G induced by sets of a-indexed walks. For such sets, we define a property called terseness and investigate how it affects the induced closure operators. We show, among others, that the induction, if regarded as a map, is one-to-one for terse walk sets. We also determine a poset of closure operators (on a given graph) that is a direct limit of a direct system of sets of terse a-indexed walks ordered by set inclusion for certain ordinals a > 1. Possible applications of the closure operators studied in digital topology are indicated.

Published
2017
Pages
258–266
Journal
Topology and its Applications, vol. 230, no. 1, ISSN 0166-8641
DOI
10.1016/j.topol.2017.08.046
UT WoS
000413130900024
EID Scopus
2-s2.0-85028932508
BibTeX 
@article{BUT144499,
  author="Josef {Šlapal}",
  title="Terse walk sets in graphs and induced closure operators",
  journal="Topology and its Applications",
  year="2017",
  volume="230",
  number="1",
  pages="258--266",
  doi="10.1016/j.topol.2017.08.046",
  issn="0166-8641",
  url="https://www.fit.vut.cz/research/publication/11591/"
}
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