Publication Details

Terse walk sets in graphs and induced closure operators

ŠLAPAL Josef. Terse walk sets in graphs and induced closure operators. Topology and Its Applications, vol. 230, no. 1, 2017, pp. 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. (RCIT FIT BUT)

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

Publisher

Elsevier Science

DOI

10.1016/j.topol.2017.08.046

UT WoS

000413130900024

EID Scopus

2-s2.0-85028932508

BibTeX

@ARTICLE{FITPUB11591,
   author = "Josef \v{S}lapal",
   title = "Terse walk sets in graphs and induced closure operators",
   pages = "258--266",
   journal = "Topology and Its Applications",
   volume = 230,
   number = 1,
   year = 2017,
   ISSN = "0166-8641",
   doi = "10.1016/j.topol.2017.08.046",
   language = "english",
   url = "https://www.fit.vut.cz/research/publication/11591"
}