Publication Details
Walk-set induced connectedness in digital spaces
Simple graph, strong product, walk, connectedness, digital space, Jordan curve theorem
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.
@ARTICLE{FITPUB11589,
author = "Josef \v{S}lapal",
title = "Walk-set induced connectedness in digital spaces",
pages = "247--256",
journal = "Carpathian Journal of Mathematics",
volume = 33,
number = 2,
year = 2017,
ISSN = "1584-2851",
language = "english",
url = "https://www.fit.vut.cz/research/publication/11589"
}