




Exponents of $r$regular primitive matrices 
MINGAI JIN, SANG GU LEE, HAN GUK SEOL 
Pages. 5157 


A Boolean matrix $A$ is said to be {f
extit{r$$regular}} if each vertex in its digraph $G(A)=G$ has
outdegree and indegree exactly $r.$ $A$ is primitive if and only
if there exist minimum integer $k$ such that $A^k>0$. For such a
matrix, its digraph $G$ is strongly connected and given any
ordered pair of vertices $x$ and $y$ there is a directed walk from
$x$ to $y$ of length $k$. Using the graph theory, we determine the
lower bounds and upper bounds of $r$regular primitive matices in
this paper. We also proved that the exponent of $r$regular
primitive tournament $T$ is just 3 and the exponent of $r$regular
primitive symmetric matrix $A$ satisfys ${
m exp}(A)leq 2(nr).$ 

1. basic concepts
2. The exponent of $r$regular primitive matrices
3. Specil $3$regular primitive matrices





