Extremal Functions on Cayley Digraphs of Finite Cyclic Groups

For positive integers d and k we define m(d, k) to be the maximum positive integer m such that the Cayley digraph of the finite cyclic group of order m, generated by a set of k positive integers has diameter less than or equal to d. In this paper we establish a new lower bound for m(2, k). We also use this lower bound to obtain a lower bound for m(d, k) for any given positive integer d and sufficiently large k.