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## Discussiones Mathematicae - General Algebra and Applications

2004 | 24 | 1 | 53-61
Tytuł artykułu

### Power indices of trace zero symmetric Boolean matrices

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
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.
Słowa kluczowe
EN
Kategorie tematyczne
Rocznik
Tom
Numer
Strony
53-61
Opis fizyczny
Daty
wydano
2004
otrzymano
2003-07-15
otrzymano
2004-01-12
Twórcy
autor
• Department of Mathematics, South China Normal University, Guangzhou 510631, P. R. China
Bibliografia
• [1] M. Gavalec, Computing matrix period in max-min algebra, Discrete Appl. Math. 75 (1997), 63-70.
• [2] D.A. Gregory, N.J. Pullman and S. Kirkland, On the dimension of the algebra generated by a Boolean matrix, Linear and Multilinear Algebra 38 (1994), 131-144.
• [3] B. Liu, B.D. McKay, N.C. Wormald, and K. Zhang, The exponent set of symmetric primitive (0,1) matrices with zero trace, Linear Algebra Appl. 133 (1990), 121-131.
• [4] S.W. Neufeld, The concept of diameter in exponents of symmetric primitive graphs, Ars Combin. 51 (1999), 129-142.
• [5] G. Ricci, Boolean matrices... neither Boolean nor matrices, Discuss. Math. Gen. Algebra Appl. 20 (2000), 141-151.
• [6] J. Shao, The exponent set of symmetric primitive matrices, Sci. Sinica Ser. A 30 (1987), 348-358.
• [7] J. Shao and Q. Li, On the index of maximum density for irreducible Boolean matrices, Discrete Appl. Math. 21 (1988), 147-156.
• [8] B. Zhou, Exponents of primitive graphs, Australas. J. Combin. 28 (2003), 67-72.
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