Korean Journal of Mathematics

The Kangwon-Kyungki Mathematical Society (강원경기수학회)
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DIAMETER OF THE DIRECT PRODUCT OF WIELANDT GRAPH

  • Kim, Sooyeon (Graduate school of Education Gangneung-wonju National University) ;
  • Song, Byung Chul (Department of Mathematics Gangneung-Wonju National University)
  • Received : 2012.08.01
  • Accepted : 2012.10.10
  • Published : 2012.12.30
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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 $W_n$ 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.

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References

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