Path-Set Induced Closure Operators on Graphs

Josef Slapal


Given a simple graph, we associate with every set of paths of the same positive length a closure operator on the (vertex set of the) graph. These closure operators are then studied. In particular, it is shown that the connectedness with respect to them is a certain kind of path connectedness. Closure operators associated with sets of paths in some graphs with the vertex set ZxZ are discussed which include the well-known Marcus-Wyse and Khalimsky topologies used in digital topology. This demonstrates possible applications of the closure operators investigated in digital image analysis.

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