Automorphism groups of digital wedges of simple k-cycles

Given a digital object with a [Formula: see text]-adjacency [Formula: see text], let [Formula: see text] be the set of [Formula: see text]-isomorphic self-functions of [Formula: see text]. Based on the group structure of [Formula: see text] under function composition, the paper investigates various properties of group structures of [Formula: see text], where [Formula: see text] is a digital wedge formulated by the two simple [Formula: see text]-cycle with [Formula: see text] elements in [Formula: see text] denoted by [Formula: see text], [Formula: see text]. Depending on the numbers [Formula: see text] and [Formula: see text] of [Formula: see text], how can we characterize the group structure of [Formula: see text]? This topic is still open. Hence, we prove that in the case [Formula: see text], [Formula: see text] is isomorphic to the typical Klein four-group. Besides, in the case [Formula: see text], [Formula: see text] is proved to be isomorphic to the typical dihedral group [Formula: see text] with eight elements. Thus, we can characterize the elements of [Formula: see text] according to the feature of the symmetry or asymmetry calculation. In this paper, we will work with [Formula: see text]-connected digital objects [Formula: see text] such that the cardinal number of [Formula: see text] is greater than or equal to [Formula: see text].