Bounds on the generalized μ-scrambling indices of primitive digraphs

Abstract

Huang and Liu [Generalized scrambling indices of primitive a digraph, Linear Algebra Appl. 433 (2010), pp. 1798–1808] gave the definitions of the generalized μ-scrambling indices and the generalized scrambling indices of a primitive digraph and also provided some exact lower and upper bounds for the generalized scrambling indices of various classes of primitive digraphs. In this paper, we give some exact lower and upper bounds for the generalized μ-scrambling indices of various classes of primitive digraphs.

Keywords:

• generalized μ-scrambling index
• generalized scrambling index
• primitive digraph
• scrambling index

2000 AMS Subject Classifications:

• 05C20
• 05C50

Acknowledgements

This research was supported by NSFC (61170311), Sichuan Province Sci. & Tech. Research Project (2009GZ0004, 2011JY0002).