On the power graphs over gyrogroups

The power graph [Formula: see text] of a group [Formula: see text] is a simple graph with the vertex set [Formula: see text] such that two distinct vertices [Formula: see text] are adjacent in [Formula: see text] if and only if [Formula: see text] or [Formula: see text], for some [Formula: see text]. The purpose of this paper is to introduce the notion of the power graph for a gyrogroup. Using this, we investigate the combinatorial properties of power graph of a gyrogroup, [Formula: see text], of order [Formula: see text] for [Formula: see text]. In particular, we determine the Hamiltonicity and planarity of the power graph of [Formula: see text]. Consequently, we calculate distance properties, resolving polynomial, independent domination polynomial, Hosoya and reciprocal Hosoya polynomials, characteristic polynomials, and the spectral radius of [Formula: see text].