Korean J. Math.
Vol 20, No 4 (2012) pp.
DIAMETER OF THE DIRECT PRODUCT OF WIELANDT GRAPH
A digraph $D$ is primitive if there is a positive integer $k$ such that there is a walk of length $k$ between arbitrary two vertices of $D$. The exponent of a primitive digraph is the least such $k$. Wielandt graph $W_n$ of order $n$ is known as the digraph whose exponent is $n^2 − 2n + 2$, which is the maximum of all the exponents of the primitive digraphs of order $n$. It is known that the diameter of the multiple direct product of a digraph $W_n$ strictly increases according to the multiplicity of the product. And it stops when it attains to the exponent of $W_n$. In this paper, we find the diameter of the direct product of Wielandt graphs.
- There are currently no refbacks.
ISSN: 1976-8605 (Print), 2288-1433 (Online)
Copyright(c) 2013 By The Kangwon-Kyungki Mathematical Society, Department of Mathematics, Kangwon National University Chuncheon 21341, Korea Fax: +82-33-259-5662 E-mail: firstname.lastname@example.org