Digital Topological Complexity of Digital Maps

TL;DR

This paper introduces digital topological complexity for digital images and maps, highlighting differences from classical topology and emphasizing the role of adjacency relations in these computations.

Contribution

It extends topological complexity concepts to digital images and maps, revealing key differences from classical topology and emphasizing adjacency relations.

Findings

Digital topological complexity computations are introduced for digital maps.

Differences between digital and classical topological complexity are revealed.

Adjacency relations significantly influence the complexity calculations.

Abstract

In this study, we improve the topological complexity computations on digital images with introducing the digital topological complexity computations of a surjective and digitally continuous map between digital images. We also reveal differences in topological complexity computations of maps between digital images and topological spaces. Moreover, we emphasize the importance of the adjacency relation on the domain and the range of a digital map in these computations.