Detail publikačního výsledku

Terse walk sets in graphs and induced closure operators

ŠLAPAL, J.

Originální název

Terse walk sets in graphs and induced closure operators

Anglický název

Terse walk sets in graphs and induced closure operators

Druh

Článek WoS

Originální abstrakt

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.

Anglický abstrakt

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.

Klíčová slova

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

Klíčová slova v angličtině

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

Autoři

ŠLAPAL, J.

Rok RIV

2018

Vydáno

01.03.2017

ISSN

0166-8641

Periodikum

TOPOLOGY AND ITS APPLICATIONS

Svazek

230

Číslo

1

Stát

Nizozemsko

Strany od

258

Strany do

266

Strany počet

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/"
}

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