Publication Details
Path-induced closure operators on graphs for defining digital Jordan surfaces
simple graph, path, closure operator, connectedness, digital space, digital surface, Khalimsky topology, Jordan surface theorem
Given a simple graph with the vertex set X, we discuss a closure operator on X induced by a set of paths with identical lengths in the graph. We introduce a certain set of paths of the same length in the 2-adjacency graph on the digital line Z and consider the closure operators on Z^m (m a positive integer) that are induced by a special product of m copies of the introduced set of paths. We focus on the case m = 3 and show that the closure operator considered provides the digital space Z^3 with a connectedness that may be used for defining digital surfaces satisfying a Jordan surface theorem.
@ARTICLE{FITPUB12120,
author = "Josef \v{S}lapal",
title = "Path-induced closure operators on graphs for defining digital Jordan surfaces",
pages = "1374--1380",
journal = "Open Mathematics",
volume = 17,
number = 1,
year = 2019,
ISSN = "2391-5455",
doi = "10.1515/math-2019-0121",
language = "english",
url = "https://www.fit.vut.cz/research/publication/12120"
}