THE SCRAMBLING INDEX OF PRIMITIVE TWO-COLORED TWO CYCLES WHOSE LENGTHS DIFFER BY 1

A two-colored digraph is a digraph each of whose arc is colored by red or blue. An -walk is a walk consisting of h red arcs and blue arcs. The scrambling index of a two-colored digraph is the smallest positive integer over all nonnegative integers h and such that for each pair of vertices u and v there is a vertex w such that there exist an -walk from u to w and an -walk from v to w. We study the scrambling index of primitive two-colored digraph consisting of two cycles whose lengths differ by 1. We present a lower bound and an upper bound for the scrambling index for such two-colored digraph. We then show that the lower and the upper bounds are sharp bounds.