Primitive digraphs with the largest scrambling index
Akelbek, Mahmud and Kirkland, Steve (2009) Primitive digraphs with the largest scrambling index. Linear Algebra and its Applications, 430 (4). pp. 1099-1110. ISSN 0024-3795
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.
Repository Staff Only: item control page