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Exponents of the primitive Boolean matrices with fixed girth

2015/06/15 by Yu, Guanglong
#Combinatorics (math.CO) #F.2.2 #FOS: Mathematics #I.2.7

paper · doi:10.48550/arxiv.1506.04459

Abstract

The girth of a primitive Boolean matrix is defined to be the girth of its associated digraph. In this paper, among all primitive Boolean matrices of order n, the primitive exponents of those of girth g are considered. For the primitive matrices of both order n≥ 10 and girth g>\fracn2-4n4(n-3), the matrices with primitive exponents in [2n-2 +(g- 1)(n-3), n+g(n-2)] are completely characterized.

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