Abstract.
Let u be a vertex of a digraph D.
Then
-
out-eccentricity of u is
e+D(u)=max{distD(u,v)
where v is a vertex of D},
-
in-eccentricity of u is
e-D(u)=max{distD(v,u)
where v is a vertex of D},
-
eccentricity of u is
eD(u)=max{e+D(u),
e-D(u)}.
The diameter of a digraph is its maximum eccentricity and the
radius is its minimum eccentricity.
A digraph D of degree t and diameter s contains at
most
Ms,t=1+t+t2+...+ts
vertices.
If it has exactly Ms,t vertices then it is called a
Moore digraph.
It is known that Moore digraphs exist only if s=1 or t=1.
If we like to have a structure "close" to Moore digraphs, we have
to relax something.
Observe that a digraph D of degree t and radius s
cannot have more than Ms,t vertices.
Therefore a digraph D is said to be radially Moore digraph if it
has degree t, the radius s, the diameter s+1 and
exactly Ms,t vertices.
In the paper we show that for each s and t there exists a
radially Moore digraph of degree t with radius s.
Moreover, we give an upper bound for the number of central vertices in radially
Moore digraphs with degree 2.