Publication detail

Path-set induced closure operators on graphs

ŠLAPAL, J.

Original Title

Path-set induced closure operators on graphs

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.

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

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

Released

29.04.2016

Location

University on Nis, Serbia

Pages from

863

Pages to

871

Pages count

9

Documents

BibTex


@article{BUT116976,
  author="Josef {Šlapal}",
  title="Path-set induced closure operators on graphs",
  annote="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.",
  chapter="116976",
  doi="10.2298/FIL1603863S",
  howpublished="print",
  number="3",
  volume="30",
  year="2016",
  month="april",
  pages="863--871",
  type="journal article in Web of Science"
}