Akelbek, Mahmud and Kirkland, Steve
Primitive digraphs with the largest scrambling index.
Linear Algebra and its Applications, 430 (4).
The scrambling index of a primitive digraph D 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 directed
walks of length k; it is denoted by k(D). In [M. Akelbek, S. Kirkland,
Coefficients of ergodicity and the scrambling index, preprint], we
gave the upper bound on k(D) in terms of the order and the girth of a
primitive digraph D. In this paper, we characterize all the primitive
digraphs suchthat the scrambling index is equal to the upper bound.
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