  The {\em power index} $\Theta(\Gamma)$ of a graph $\Gamma$ is the least order
of a group $G$ such that $\Gamma$ can embed into the power graph of $G$.
Furthermore, this group $G$ is {\em $\Gamma$-optimal} if $G$ has order
$\Theta(\Gamma)$. We say that $\Gamma$ is {\em power-critical} if its order
equals to $\Theta(\Gamma)$. This paper focuses on the power indices of complete
graphs, complete bipartite graphs and $1$-factors. We classify all
power-critical graphs $\Gamma'$ in these three families, and give a necessary
and sufficient condition for $\Gamma'$-optimal groups.
