Imprimitive non-powerful sign pattern matrices with maximum base

Abstract

You et al. [L.H. You, J.Y. Shao, and H.Y. Shan, Bounds on the bases of irreducible generalized sign pattern matrices, Linear Algebra Appl. 427 (2007), pp. 285–300], obtained an upper bound of the bases for imprimitive non-powerful sign pattern matrices. In this article, we characterize those imprimitive non-powerful sign pattern matrices whose bases reach this upper bound.

Keywords:

• sign pattern
• signed digraph
• base
• powerful
• imprimitive

AMS Subject Classifications::

• 15A33
• 05C22
• 05C50

Acknowledgements

The authors would like to thank the referees for many helpful comments and suggestions leading to the clear presentation of the article. The project is supported by NSFC (10871166), NSF of Jiangsu province (BK2007030), NSF of University in Jiangsu province (07KJD110207) and NSF of Xuzhou Normal University (08XLB01).