Galois connections between sets of paths and closure operators in simple graphs

Galois connections between sets of paths and closure operators in simple graphs

WoS Article

For every positive integer n,we introduce and discuss an isotone Galois connection between the sets of paths of lengths n in a simple graph and the closure operators on the (vertex set of the) graph.We consider certain sets of paths in a particular graph on the digital line Z and study the closure operators associated, in the Galois connection discussed, with these sets of paths. We also focus on the closure operators on the digital plane Z^2 associated with a special product of the sets of paths considered and show that these closure operators may be used as background structures on the plane for the study of digital images.

For every positive integer n,we introduce and discuss an isotone Galois connection between the sets of paths of lengths n in a simple graph and the closure operators on the (vertex set of the) graph.We consider certain sets of paths in a particular graph on the digital line Z and study the closure operators associated, in the Galois connection discussed, with these sets of paths. We also focus on the closure operators on the digital plane Z^2 associated with a special product of the sets of paths considered and show that these closure operators may be used as background structures on the plane for the study of digital images.

Simple graph, Closure operator, Galois connection, digital space, Khalimsky topology, Jordan curve theorem.

Simple graph, Closure operator, Galois connection, digital space, Khalimsky topology, Jordan curve theorem.

ŠLAPAL, J.

2019

31.12.2018

2391-5455

Open Mathematics

16

1

Republic of Poland

1573

1581

9

https://www.degruyter.com/downloadpdf/j/math.2018.16.issue-1/math-2018-0128/math-2018-0128.pdf

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