  The average distance of a vertex $v$ of a connected graph $G$ is the
arithmetic mean of the distances from $v$ to all other vertices of $G$. The
proximity $\pi(G)$ and the remoteness $\rho(G)$ of $G$ are the minimum and the
maximum of the average distances of the vertices of $G$, respectively.
  In this paper, we give upper bounds on the remoteness and proximity for
graphs of given order, minimum degree and maximum degree. Our bounds are sharp
apart from an additive constant.
