‎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 $n > 1$‎. Manuscript profile

‎In this study‎, ‎we delve into the discrete TC of surjective simplicial fibrations‎, ‎aiming to unravel the interplay between topological complexity‎, ‎discrete geometric structures‎, ‎and computational efficiency‎. ‎Moreover‎, ‎we examine the properties of the discrete TC number in higher dimensions and its relationship with scat‎. ‎We also touch on the basic properties of the notion of higher contiguity distance and show that it is possible to consider discrete TC computations in a simpler sense‎. Manuscript profile