Detail výsledku
Walk-set induced connectedness in digital spaces
In an undirected simple graph, we define connectedness induced by a set of walks of the same lengths. We show that the connectedness is preserved by the strong product of graphs with walk sets. This result is used to introduce a graph on the vertex set Z^2 with sets of walks that is obtained as the strong product of a pair of copies of a graph on the vertex set Z with certain walk sets. It is proved that each of the walk sets in the graph introduced induces connectedness on Z^2 that satisfies a digital analogue of the Jordan curve theorem. It follows that the graph with any of the walk sets provides a convenient structure on the digital plane Z^2 for the study of digital images.
Simple graph, strong product, walk, connectedness, digital space, Jordan curve theorem
@article{BUT144498,
author="Josef {Šlapal}",
title="Walk-set induced connectedness in digital spaces",
journal="Carpathian Journal of Mathematics",
year="2017",
volume="33",
number="2",
pages="247--256",
issn="1584-2851",
url="http://carpathian.ubm.ro"
}