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.