Primitive digraphs with the largest scrambling index

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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;
Academic Unit:	Faculty of Science and Engineering > Research Institutes > 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
Related URLs:	http://www.sciencedirect.com/science/jou...
URI:	https://mural.maynoothuniversity.ie/id/eprint/2061
Use Licence:	This item is available under a Creative Commons Attribution Non Commercial Share Alike Licence (CC BY-NC-SA). Details of this licence are available here

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Primitive digraphs with the largest scrambling index

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