Connected sum of digital closed surfaces

During the past 20 years the research of digital surfaces has proceeded to find their properties in the digital space Zn, such as a topological number, a simple k-point, the 3D-Jordan theorem, a k-separating set, a boundary detecting algorithm and so on. Actually, unlike surfaces in a continuous space, the features of digital surfaces have different characteristics. The aim of this paper is to introduce the notion of a digital closed k-surface in Zn, n ⩾ 3, with the general k-adjacency relations as a generalization of Malgouyres’ and Morgenthaler’s k-surfaces in Z3, to establish some minimal simple closed k-surfaces in Z3 and to find their digital topological properties in relation with the k-fundamental group and k-contractibility. Moreover, a connected sum of two digital closed surfaces is introduced and its digital topological properties are investigated.