  We report the observation of a distinct correlation between the kinetic
fragility index $m$ and the reduced Arrhenius crossover temperature $\theta_A =
T_A/T_g$ in various glass-forming liquids, identifying three distinguishable
groups. In particular, for 11 glass-forming metallic liquids, we universally
observe a crossover in the mean diffusion coefficient from high-temperature
Arrhenius to low-temperature super-Arrhenius behavior at approximately
$\theta_A \approx 2$ which is in the stable liquid phases. In contrast, for
fragile molecular liquids, this crossover occurs at much lower $\theta_A
\approx 1.4$ and usually in their supercooled states. The $\theta_A$ values for
strong network liquids spans a wide range higher than 2. Intriguingly, the
high-temperature activation barrier $E_\infty$ is universally found to be $\sim
11\ k_B T_g$ and uncorrelated with the fragility or the reduced crossover
temperature $\theta_A$ for metallic and molecular liquids. These observations
provide a way to estimate the low-temperature glassy characteristics ($T_g$ and
$m$) from the high-temperature liquid quantities ($E_\infty$ and $\theta_A$).
