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{BUT162077,
author="Josef {Šlapal}",
title="Path-induced closure operators on graphs for defining digital Jordan surfaces",
journal="Open Mathematics",
year="2019",
volume="17",
number="1",
pages="1374--1380",
doi="10.1515/math-2019-0121",
issn="2391-5455",
url="https://www.degruyter.com/view/j/math.2019.17.issue-1/math-2019-0121/math-2019-0121.xml?format=INT"
}