Abstract
In a simple undirected graph, we introduce a special connectedness induced by a set of paths of length 2. We focus on the 8-adjacency graph (with the vertex set \(\mathbb {Z}^2\)) and study the connectedness induced by a certain set of paths of length 2 in the graph. For this connectedness, we prove a digital Jordan curve theorem by determining the Jordan curves, i.e., the circles in the graph that separate \(\mathbb {Z}^2\) into exactly two connected components. These Jordan curves are shown to have an advantage over those given by the Khalimsky topology on \(\mathbb {Z}^2\).
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