Acta Mathematicae Applicatae Sinica

, Volume 13, Issue 4, pp 410–413 | Cite as

The diameters of almost all Cayley digraphs

  • Meng Jixiang 
  • Liu Xin 


LetG be a finite group of ordern andS be a subset ofG not containing the identity element ofG. Letp (0<p<1) be a fixed number. We define the set of all labelled Cayley digraphsX(G,S) (S<-G\{1}) ofG as a sample space and assign a probability measure by requiringP(aεS)=p for anyaG\{1}. Here it is shown that the probability of the set of Cayley digraphs ofG with diameter 2 approaches 1 as the ordern ofG approaches infinity.

Key words

Random Cayley digraph 


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Copyright information

© Science Press, Beijing, China and Allerton Press, Inc., New York, U.S.A. 1997

Authors and Affiliations

  • Meng Jixiang 
    • 1
  • Liu Xin 
    • 2
  1. 1.Department of MathematicsXinjiang UniversityUrumqiChina
  2. 2.Institute of Applied Mathematicsthe Chinese Academy of SciencesBeijingChina

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