Terse walk sets in graphs and induced closure operators

Terse walk sets in graphs and induced closure operators

WoS Article

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.

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.

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

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

ŠLAPAL, J.

2018

01.03.2017

0166-8641

TOPOLOGY AND ITS APPLICATIONS

230

1

Kingdom of the Netherlands

258

266

9

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

TopAppl2017