The degree-diameter problem asks for the maximum number of vertices in a
graph with maximum degree Ξ and diameter k. For fixed k, the answer
is Ξ(Ξk). 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 Ξ(Ξkβ1), 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