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Full-Text Articles in Physical Sciences and Mathematics
Digital Topological Complexity Numbers, İsmet Karaca, Meli̇h İs
Digital Topological Complexity Numbers, İsmet Karaca, Meli̇h İs
Turkish Journal of Mathematics
The intersection of topological robotics and digital topology leads to us a new workspace. In this paper we introduce the new digital homotopy invariant digital topological complexity number $TC(X,\kappa)$ for digital images and give some examples and results about it. Moreover, we examine adjacency relations in the digital spaces and observe how $TC(X,\kappa)$ changes when we take a different adjacency relation in the digital spaces.
Digital Lusternik-Schnirelmann Category, Ayse Borat, Tane Vergi̇li̇
Digital Lusternik-Schnirelmann Category, Ayse Borat, Tane Vergi̇li̇
Turkish Journal of Mathematics
In this paper, we define the digital Lusternik-Schnirelmann category cat${}_\kappa$, introduce some of its properties, and discuss how the adjacency relation affects the digital Lusternik-Schnirelmann category.