Matrices with maximum kth local exponent in the class of doubly symmetric primitive matrices |
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Authors: | Shexi Chen Bolian Liu |
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Institution: | a School of Mathematics and Computational Science, Hunan University of Science and Technology, Xiangtan, Hunan 411201, PR China b Department of Mathematics, South China Normal University, Guangzhou 510631, PR China |
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Abstract: | Let A be a primitive matrix of order n, and let k be an integer with 1?k?n. The kth local exponent of A, is the smallest power of A for which there are k rows with no zero entry. We have recently obtained the maximum value for the kth local exponent of doubly symmetric primitive matrices of order n with 1?k?n. In this paper, we use the graph theoretical method to give a complete characterization of those doubly symmetric primitive matrices whose kth local exponent actually attain the maximum value. |
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Keywords: | 05C50 15A33 |
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