The minimum order of n-connected n-regular graphs with specified diameters

In this paper, an exact formula for the order of a minimum
(d, n, n)
-graph, for any
n
and
d
, is derived, and an algorithm to construct a class of minimum
(d, n, n)
-graphs is presented. For the case
n = 3
, this formula yields the result obtained by Myers for the order of minimum
(d, 3,3)
-graphs.