Behzad, Chartrand and Wall proposed the conjecture that any regular directed graph of degree \(r\) and girth \(g\) has order \(n\geq r(g- 1)+ 1\). The main result is the following theorem: Let \(X= \text{Cay}(G, S)\) be a connected Abelian Cayley digraph with girth \(g> 3\), degree \(r\), and order \(n\). Then \(n\geq (r+ 1)(g- 1)- 1\) unless \(X\) is a lexicographic product of a family of Cayley digraphs on \(\text{Z}_{n_ i}\), \(1\geq i\geq k\), defined by subsets of the form \(\{x: 1\geq x\geq s_ i\}\), where \(0\geq s_ i\geq n_ i\) and \(n= n_ 1\cdots n_ k\). This bound is best possible.