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 
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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