The Scrambling Indices of Primitive Digraphs with Exactly Two Cycles

Abstract

In 2009, Akelbek and Kirkland introduced a useful parameter called the scrambling index of a primitive digraph $D$, which is the smallest positive integer $k$ such that for every pair of vertices $u$ and $v$, there is a vertex $w$ such that we can get to $w$ from $u$ and $v$ in $D$ by walks of length $k$. In this paper, we study and obtain the scrambling indices of all primitive digraphs with exactly two cycles.