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

Open Mathematics

Šlapal Josef¹ 

[1] IT4Innovations Centre of Excellence, Brno University of Technology, 612 66Brno, Czech Republic;

关键词: simple graph;    closure operator;    galois connection;    digital space;    khalimsky topology;    jordan curve theorem;    05c10;    54a05;    54d05;   

DOI  :  10.1515/math-2018-0128

来源: DOAJ

【 摘 要 】

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 Z2 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.

【 授权许可】

Unknown