Path-induced closure operators on graphs for defining digital Jordan surfaces
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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.
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2021 ◽
Vol 2021
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pp. 1-9
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2012 ◽
Vol 04
(01)
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pp. 1250006
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2018 ◽
Vol 17
(12)
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pp. 1850234
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Keyword(s):
2018 ◽
Vol 10
(2)
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pp. 9