A note on the coprime power graph of groups

Abstract Some years ago, Shitov proved that the chromatic number of the power graph of semi-groups is at most countable, thus answering a question raised by Aalipour et al. about whether this statement holds for groups. Later, Dalal and Kumar proved that the chromatic number of the enhanced power graph of a group is also countable. In the line of these recent works, we first generalize the concept of power graphs to coprime power graph, and then we prove the same type of result for this generalization. Furthermore, we state a conjecture about their common relationship as graphs.