DM-GAA

ISSN 1509-9415 (print version)

ISSN 2084-0373 (electronic version)

https://doi.org/10.7151/dmgaa

Discussiones Mathematicae - General Algebra and Applications

Cite Score (2023): 0.6

SJR (2023): 0.214

SNIP (2023): 0.604

Index Copernicus (2022): 121.02

H-Index: 5

Discussiones Mathematicae - General Algebra and Applications

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Discussiones Mathematicae General Algebra and Applications 24(1) (2004) 53-61
DOI: https://doi.org/10.7151/dmgaa.1075

POWER INDICES OF TRACE ZERO SYMMETRIC BOOLEAN MATRICES

Bo Zhou

Department of Mathematics,
South China Normal University,
Guangzhou 510631, P. R. China

e-mail: zhoubo@scnu.edu.cn

Abstract

The power index of a square Boolean matrix A is the least integer d such that Ad is a linear combination of previous nonnegative powers of A. We determine the maximum power indices for the class of n×n primitive symmetric Boolean matrices of trace zero, the class of n×n irreducible nonprimitive symmetric Boolean matrices, and the class of n×n reducible symmetric Boolean matrices of trace zero, and characterize the extreme matrices respectively.
Keywords: power index, index of convergence, period, Boolean matrix.
2000 Mathematics Subject Classification: 15A33, 05C50.

References

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Received 15 July 2003
Revised 12 January 2004


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