Path-set induced closure operators on graphs | Zendy

Josef Šlapal | Zendy

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Path-set induced closure operators on graphs

Author(s) -

Josef Šlapal

Publication year - 2016

Publication title -

filomat

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.449

H-Index - 34

eISSN - 2406-0933

pISSN - 0354-5180

DOI - 10.2298/fil1603863s

Subject(s) - mathematics , closure (psychology) , social connectedness , vertex (graph theory) , closure operator , discrete mathematics , operator (biology) , path (computing) , topology (electrical circuits) , combinatorics , graph , closed set , computer science , psychology , biochemistry , chemistry , repressor , economics , transcription factor , market economy , psychotherapist , gene , programming language

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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