Adjacencies for recognition of digital Jordan surfaces

For every positive integer, we introduce an adjacency in the digital space \({\mathbb {Z}}^3\) ${\mathbb{Z}}^3$ . Connectedness in the graph obtained is then used to define and study digital Jordan surfaces. The surfaces are acquired as polyhedral surfaces bounding the digital polyhedra that can be face-to-face tiled with digital cubes, triangular prisms, square pyramids, and tetrahedra.