  As an interesting application of the Einstein-Gauss-Bonnet theory and our
work on the Gauss-Bonnet-Chern mass (Ge, Wang, Wu), we obtain a positive mass
theorem for asymptotically flat graphs in $\R^{n+1}$ under a condition that
$R+\alpha L_2$ is non-negative, where $R$ is the scalar curvature,
$\alpha\in\R$ a constant and $L_2$ the second Gauss-Bonnet curvature. A Penrose
type inequality is also obtained in the case $\alpha>0$.
