Structuring Digital Spaces by Path-Partition Induced Closure Operators on Graphs

摘要

We study closure operators on graphs which are induced by path partitions, i.e., certain sets of paths of the same lengths in these graphs. We investigate connectedness with respect to the closure operators studied. In particular, the closure operators are discussed that are induced by path partitions of some natural graphs on the digital spaces Z~n, n > 0 a natural number. For the case n = 2, i.e., for the digital plane Z~2, the induced closure operators are shown to satisfy an analogue of the Jordan curve theorem, which allows using them as convenient background structures for studying digital images.