Relation between rad(G) , Δ(G) and |G| in a graph Is there a formula for resolving the following question : "Given a graph G with rad(G) = 3 and Δ(G) = 5, can we have |G| = 2006?" 

rad(G) is  is the minimum graph eccentricity of any vertex in G.(The eccentricity is the maximum graph between v and any other vertex u of G)

Δ(G) is the maximum degree in G(a degree of a vertex is the nr. of edges at it)

|G| is the nr. of vertices

I was thinking using the theorem "The number of vertices of odd degree in any graph G is even". By this, it can be |G| = 2006 if Δ(G) = 5, but how can I use the rad(G) as well?
Note that in a graph of maximum degree $d$, for a fixed vertex $v$ there are 


at most $d$ vertexes at distance $1$ from $v$,   
at most $d(d-1)$ vertexes at distance $2$ from $v$, 
at most $d(d-1)^2$ vertexes at distance $3$ from $v$,
and so on.


Take $v$ a vertex that is a "center" so has distance at most $3$ to each other vertex and do the calculation. (Do not forget $v$ itself.)
If it is radius = 3  and diameter = 5 according to

http://www.sciencedirect.com/science/article/pii/0012365X73901167

there is no reason why such a graph could not be constructed.