Categorical aspects of inducing closure operators on graphs by sets of walks
作者：
Highlights：
• An original way of inducing closure operators on graphs.
• Proving that the induction constitutes a categorical Galois correspondence.
• Characterizing the closure operators that are induced on a graph by a path set.
• Showing that the closure operators induced generalize the Khalimsky and Marcus–Wyse topologies.
• Indicating a possible use of the closure operators as base structures on the digital plane for the study of digital images.
摘要
•An original way of inducing closure operators on graphs.•Proving that the induction constitutes a categorical Galois correspondence.•Characterizing the closure operators that are induced on a graph by a path set.•Showing that the closure operators induced generalize the Khalimsky and Marcus–Wyse topologies.•Indicating a possible use of the closure operators as base structures on the digital plane for the study of digital images.
论文关键词：Simple graph,Walk,Closure operator,Galois correspondence between concrete categories,Diagonal walk set,Digital topology
论文评审过程：Received 30 August 2016, Revised 2 January 2017, Accepted 18 February 2017, Available online 7 March 2017, Version of Record 30 April 2018.
论文官网地址：https://doi.org/10.1016/j.jcss.2017.02.005
