Path-induced closure operators on graphs for defining digital Jordan surfaces
| Autor: | Josef Šlapal |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2019 |
| Předmět: |
Social connectedness
General Mathematics Closure (topology) digital surface 54a05 01 natural sciences connectedness digital space QA1-939 Closure operator simple graph 0101 mathematics Geometry and topology Mathematics Discrete mathematics jordan surface theorem Simple graph 68r10 010102 general mathematics path 52c99 010101 applied mathematics 54d05 Path (graph theory) Digital surface khalimsky topology closure operator MathematicsofComputing_DISCRETEMATHEMATICS |
| Zdroj: | Open Mathematics, Vol 17, Iss 1, Pp 1374-1380 (2019) |
| ISSN: | 2391-5455 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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