The minimum-order three-connected cubic graphs with specified diameters

A minimum
(d,c, \upsilon )
-graph is one which is regular of degree
\upsilon
, has diameter
d
and connectivity
c
, and is of minimum order, i.e., has the minimum number of points. Such graphs have application in the design of survivable communications networks. The minimum order of a
(d, 3,3)
-graph is determined, and the construction of all minimum
(d, 3,3)
-graphs is described.