In order to avoid trivialities, it is assumed throughout that d 22, vacal, and ~23. A (d, c, v)-graph is a c-connected graph of diameter d in which each node is of valence v. The minimum order (number of nodes) of such graphs is denoted by p(d, c, v), and a minimum (d, c, v)-graph is one of minimum order. The minimum (d, 1,3)-graphs and minimum (d, 2,3)-graphs were classified and enumerated by Klee and Quaife [6], and for odd d the minimum (d, 3,3)-graphs were classified and enumerated by Klee [4]. Related results were published by Myers (7-91. For large values of c and v, it seems hopeless to attempt to classify all minimum (d, c, v)-graphs, and precise enumeration seems also to be very difficult. However, it is possible to determine p(d, c, v) for all (d, c, v), and that is the purpose of the present note. Obviously &!, c, v) 2 p (d, c, v), the minimum order of a c-connected graph of diameter at least d in which each node is of valence at least v. It turns out that in many cases ,p(d,c,v) = p( d,c,v), where this means that the two function values differ by as little as possible, taking into account the fact that all odd-valent graphs are of the L . ._ -J-I order (in other words, either p(d, c, v) = ~(d, c, v), or v and p( d, c, v) are both odd andp(d, c, v) = p( d, c, v) + 1). However, there are cases in which the excess of p(d, c, v) over F( d, c, v) is not accounted for by this