  The power graph $P(G)$ of a group $G$ is a simple graph with the vertex set
$G$ such that two distinct vertices $u,v \in G$ are adjacent in $P(G)$ if and
only if $u^m = v$ or $v^m = u$, for some $m \in \mathbb{N}$. The purpose of
this paper is to introduce the notion of a power graph for gyrogroups. Using
this, we investigate the combinatorial properties of a certain gyrogroup, say
$G(n)$, of order $2^n$ for $n \geq 3$. In particular, we determine the
Hamiltonicity and planarity of the power graph of $G(n)$. Consequently, we
calculate distant properties, resolving polynomial, Hosoya and reciprocal
Hosoya polynomials, characteristic polynomials, and the spectral radius of the
power graph of $G(n)$.
