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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

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Abstract

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.

Item Type: Article
Keywords: Scrambling index; Primitive digraph;
Subjects: Science & Engineering > Hamilton Institute
Item ID: 2061
Depositing User: Professor Steve Kirkland
Date Deposited: 21 Jul 2010 13:53
Journal or Publication Title: Linear Algebra and its Applications
Publisher: Elsevier
Refereed: Yes
URI:

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