Publication detail

Path-set induced closure operators on graphs

ŠLAPAL, J.

Czech title

Uzávěrové operace na grafech indukované množinami cest

English title

Path-set induced closure operators on graphs

Type

journal article in Web of Science

Language

en

Original abstract

Given a simple graph, we associate with every set of paths of the same positive length a closure operator on the (vertex set of the) graph. These closure operators are then studied. In particular, it is shown that the connectedness with respect to them is a certain kind of path connectedness. Closure operators associated with sets of paths in some graphs with the vertex set Z^2 are discussed which include the well known Marcus-Wyse and Khalimsky topologies used in digital topology.

Czech abstract

V daném grafu asociujeme s každou nnožinou cest stejné pozitivní délky uzávěrový operátor na množině vrcholů tohoto grafu. Tyto uzávěrové operátory jsou pak studovány. Kromě jiného je ukázáno, že souvislost vzhledem k nim je jistým druhem cestové souvislosti. Uzávěrové operátory asociované s množinami cest v jistých grafech s množinou vrcholů Z^2 jsou diskutovány. Tyto uzávěrové oparátory zahrnují známé Marcus-Wyseho a Khalimského topologie, které jsou užívány v digitální topologii.

English abstract

Given a simple graph, we associate with every set of paths of the same positive length a closure operator on the (vertex set of the) graph. These closure operators are then studied. In particular, it is shown that the connectedness with respect to them is a certain kind of path connectedness. Closure operators associated with sets of paths in some graphs with the vertex set Z^2 are discussed which include the well known Marcus-Wyse and Khalimsky topologies used in digital topology.

Keywords in Czech

Jednoduchý graf, cesta, uzávěrový operátor, souvislost, Mascus-Wyseho a Khalimského topologie.

Keywords in English

Simple graph, path, closure operator, connectedness, Marcus-Wyse and Khalimsky topologies

Released

29.04.2016

Location

University on Nis, Serbia

ISSN

0354-5180

Volume

30

Number

3

Pages from–to

863–871

Pages count

9

BIBTEX


@article{BUT116976,
  author="Josef {Šlapal},
  title="Path-set induced closure operators on graphs",
  year="2016",
  volume="30",
  number="3",
  month="April",
  pages="863--871",
  address="University on Nis, Serbia",
  issn="0354-5180"
}