A digital Jordan surface theorem with respect to a graph connectedness

Abstract

After introducing a graph connectedness induced by a given set of paths of the same length, we focus on the 2-adjacency graph on the digital line Z{\mathbb{Z}} with a certain set of paths of length nn for every positive integer nn. The connectedness in the strong product of three copies of the graph is used to define digital Jordan surfaces. These are obtained as polyhedral surfaces bounding the polyhedra that can be face-to-face tiled with digital tetrahedra.

Keywords

• simple graph
• strong product
• path
• connectedness
• digital space
• jordan surface
• 52c22
• 68r10