Power graph of finite abelian groups

Let $G$ be a group. The power graph $\Gamma_P(G)$ of $G$ is a graph with vertex set $V(\Gamma_P(G)) = G$ and two distinct vertices $x$ and $y$ are adjacent in $\Gamma_P(G)$ if and only if either $x^i=y$ or $y^j=x$, where $2\leq i,j \leq n$. In this paper, we obtain some fundamental characterizations of the power graph. Also, we characterize certain classes of power graphs of finite abelian groups.