The Concept of Diameter in Exponents of Symmetric Primitive Graphs

Abstract

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 $k$.