Korean J. Math. Vol. 20 No. 4 (2012) pp.395-402
DOI: https://doi.org/10.11568/kjm.2012.20.4.395

DIAMETER OF THE DIRECT PRODUCT OF WIELANDT GRAPH

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Sooyeon Kim
Byung Chul Song

Abstract

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 Wn of order n is known as the digraph whose exponent is n22n+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 Wn strictly increases according to the multiplicity of the product. And it stops when it attains to the exponent of Wn. In this paper, we find the diameter of the direct product of Wielandt graphs.


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