Korean Journal of Mathematics

The Kangwon-Kyungki Mathematical Society (강원경기수학회)
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CLASSIFICATION OF TWO-REGULAR DIGRAPHS WITH MAXIMUM DIAMETER

  • Kim, Byeong Moon (Department of Mathematics Gangneung-Wonju National University) ;
  • Song, Byung Chul (Department of Mathematics Gangneung-Wonju National University) ;
  • Hwang, Woonjae (Department of Information and Mathematics Korea University)
  • Received : 2012.04.29
  • Accepted : 2012.06.15
  • Published : 2012.06.30
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Abstract

The Klee-Quaife problem is finding the minimum order ${\mu}(d,c,v)$ of the $(d,c,v)$ graph, which is a $c$-vertex connected $v$-regular graph with diameter $d$. Many authors contributed finding ${\mu}(d,c,v)$ and they also enumerated and classied the graphs in several cases. This problem is naturally extended to the case of digraphs. So we are interested in the extended Klee-Quaife problem. In this paper, we deal with an equivalent problem, finding the maximum diameter of digraphs with given order, focused on 2-regular case. We show that the maximum diameter of strongly connected 2-regular digraphs with order $n$ is $n-3$, and classify the digraphs which have diameter $n-3$. All 15 nonisomorphic extremal digraphs are listed.

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References

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