The Concept of Diameter in Exponents of Symmetric Primitive Graphs

A directed graph \(G\) is primitive if there exists a positive integer \(k\) such that for every pair \(u, v\) of vertices of \(G\) there is a walk from \(u\) to \(v\) of length \(k\). The least such \(k\) is called the exponent of \(G\). The exponent set \(E_n\) is the set of all integers \(k\) such that there is a primitive graph \(G\) on \(n\) vertices whose exponent is \(k\).