  The degree-diameter problem asks for the maximum number of vertices in a
graph with maximum degree $\Delta$ and diameter $k$. For fixed $k$, the answer
is $\Theta(\Delta^k)$. We consider the degree-diameter problem for particular
classes of sparse graphs, and establish the following results. For graphs of
bounded average degree the answer is $\Theta(\Delta^{k-1})$, and for graphs of
bounded arboricity the answer is $\Theta(\Delta^{\floor{k/2}})$, in both cases
for fixed $k$. For graphs of given treewidth, we determine the the maximum
number of vertices up to a constant factor. More precise bounds are given for
graphs of given treewidth, graphs embeddable on a given surface, and
apex-minor-free graphs.
