Year: 2015
Type: preprint
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 $n\geq 10$ and girth $g>\frac{n^{2}-4n}{4(n-3)}$, the matrices with primitive exponents in $[2n-2 +(g- 1)(n-3), n+g(n-2)]$ are completely characterized.
Source: arXiv (Cornell University)
Author: Yu, Guanglong
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2292629343