The Scrambling Index of a Class of Two-colored Hamiltonian Digraphs

The scrambling index of a two-colored digraph is the least positive integer h + l over all pairs of nonnegative integers (h,l) such that for each pair of vertices u and v there is a vertex If with the property that there exist a walk from u to If and a walk from v to If that consist of h red arcs and l blue arcs. We discuss the scrambling index of a class of two-colored Hamiltonian digraphs on n >= 5 odd vertices with two cycles of length n and (n-1)/2, respectively. We present formulae for scrambling index of such two-colored Hamiltonian digraph that depend on n and the position of the blue arcs relative to the vertex of indegree 2.