Abstract
A digraph D is primitive if there is a positive integer <TEX>$k$</TEX> such that there is a walk of length <TEX>$k$</TEX> between arbitrary two vertices of D. The exponent of a primitive digraph is the least such <TEX>$k$</TEX>. Wielandt graph <TEX>$W_n$</TEX> of order <TEX>$n$</TEX> is known as the digraph whose exponent is <TEX>$n^2-2n+2$</TEX>, 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 <TEX>$W_n$</TEX> strictly increases according to the multiplicity of the product. And it stops when it attains to the exponent of <TEX>$W_n$</TEX>. In this paper, we find the diameter of the direct product of Wielandt graphs.
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