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The diameters of almost all Cayley digraphs

The diameters of almost all Cayley digraphs 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 anya∈G\{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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Mathematicae Applicatae Sinica Springer Journals

The diameters of almost all Cayley digraphs

Acta Mathematicae Applicatae Sinica , Volume 13 (4) – Jul 13, 2005

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Publisher
Springer Journals
Copyright
Copyright © 1997 by Science Press, Beijing, China and Allerton Press, Inc., New York, U.S.A.
Subject
Mathematics; Applications of Mathematics; Math Applications in Computer Science; Theoretical, Mathematical and Computational Physics
ISSN
0168-9673
eISSN
1618-3932
DOI
10.1007/BF02009550
Publisher site
See Article on Publisher Site

Abstract

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 anya∈G\{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.

Journal

Acta Mathematicae Applicatae SinicaSpringer Journals

Published: Jul 13, 2005

References