Path-induced closure operators on graphs for defining digital Jordan surfaces

Abstract

Given a simple graph with the vertex set X, we discuss a closure operator on X induced by a set of paths with identical lengths in the graph. We introduce a certain set of paths of the same length in the 2-adjacency graph on the digital line ℤ and consider the closure operators on ℤm (m a positive integer) that are induced by a special product of m copies of the introduced set of paths. We focus on the case m = 3 and show that the closure operator considered provides the digital space ℤ3 with a connectedness that may be used for defining digital surfaces satisfying a Jordan surface theorem.

Keywords

• simple graph
• path
• closure operator
• connectedness
• digital space
• digital surface
• khalimsky topology
• jordan surface theorem
• 54a05
• 54d05
• 52c99
• 68r10