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 with sets of walks that is obtained as the strong product of a pair of copies of a graph on the vertex set
with certain walk sets. It is proved that each of the walk sets in the graph introduced induces connectedness on
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
for the study of digital images.
Walk-set induced connectedness in digital spaces
Šlapal, Josef
Abstract

Additional Information
Author(s) | Šlapal, Josef |
---|