Geodesic
Power indices of trace zero symmetric Boolean matrices
Discussiones Mathematicae. General Algebra and Applications, Tome 24 (2004) no. 1, pp. 53-61.

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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 
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Zhou, Bo. Power indices of trace zero symmetric Boolean matrices. Discussiones Mathematicae. General Algebra and Applications, Tome 24 (2004) no. 1, pp. 53-61. http://geodesic.mathdoc.fr/item/DMGAA_2004_24_1_a3/

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