  This paper considers the degree-diameter problem for extremal and largest
known undirected circulant graphs of degree 2 to 9 of arbitrary diameter. As
these graphs are vertex transitive it is possible to define their distance
partition. The number of vertices in each level of the distance partition is
shown to be related to an established upper bound for the order of Abelian
Cayley graphs. Furthermore these graphs are all found to have odd girth which
is maximal for their diameter. Therefore the type of each vertex in a level may
be well-defined by the number of adjacent vertices in the preceding level. With
this definition the number of vertices of each type in each level is also shown
to be related to the same Abelian Cayley graph upper bound. Finally some
implications are discussed for circulant graphs of higher degree.
