Topological complexities of finite digital images

Subject Areas : Algebraic topology

M. Is ¹ , I. Karaca ²

1 - Department of Mathematics, Faculty of Science, Ege University, Izmir, Turkey
2 - Department of Mathematics, Faculty of Science, Ege University, Izmir, Turkey

Received: 2022-02-12 Accepted : 2022-03-30 Published : 2022-03-30

Keywords: Topological complexity, higher topological complexity, digital topology,

Abstract :

‎Digital topological methods are often used in computing the topological complexity of digital images‎. ‎We give new results on the relation between reducibility and digital contractibility in order to determine the topological complexity of a digitally connected finite digital image‎. ‎We present all possible cases of the topological complexity TC of a finite digital image in $\mathbb{Z}$ and $\mathbb{Z}^{2}$‎. ‎Finally‎, ‎we determine the higher topological complexity TC$_{n}$ of finite irreducible digital images independently of the number of points for $n > 1$‎.

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