Are there positive integers $\Delta, d$ such that the following statement is true?



> 
> 
> > 
> > For every $n\in \mathbb{N}$ there is a graph $G = (V,E)$ such that $|V| = n$, 
> >  $\Delta(G) \leq \Delta$ (where $\Delta(G)$ is the maximum degree of $G$), and
> >  $\text{diam}(G) \leq d$.
> > 
> > 
> > 
> 
> 
> 



Is the number of vertices bounded for fixed max degree and fixed diameter?
A graph of maximum degree $\leq \Delta$, and diameter $\leq d$ can have at most
$1+\Delta\sum\_{i=0}^{d-1} (\Delta-1)^i$ vertices. The graphs which attain this bound are called [Moore graphs](http://en.wikipedia.org/wiki/Moore_graph#Bounding_vertices_by_degree_and_diameter).


