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 w with the property that there exist a walk from u to w and a walk from v to w 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.
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