Publication detail

Terse walk sets in graphs and induced closure operators

ŠLAPAL, J.

Original Title

Terse walk sets in graphs and induced closure operators

Type

journal article in Web of Science

Language

English

Original 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.

Keywords

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

Authors

ŠLAPAL, J.

Released

1. 3. 2017

ISBN

0166-8641

Periodical

Topology and its Applications

Year of study

230

Number

1

State

Kingdom of the Netherlands

Pages from

258

Pages to

266

Pages count

9

URL

https://www.fit.vut.cz/research/publication/11591/

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/"
}