A Digital Index Theorem

This paper is devoted to prove a Digital Index Theorem for digital (n − 1)-manifolds in a digital space (Rn, f), where f belongs to a large family of lighting functions on the standard cubical decomposition Rn of the n-dimensional Euclidean space. As an immediate consequence we obtain the corresponding theorems for all (α, β)-surfaces of Kong-Roscoe, with α, β ∈ {6, 18, 26} and (α, β) 6= (6, 6), (18, 26), (26, 26), as well as for the strong 26-surfaces of Bertrand-Malgouyres.