Lladser, Manuel E.; Potočnik, Primož; Širáň, Jozef and WIlson, Mark C.
(2012).
*Discrete Mathematics and Theoretical Computer Science*, 14(2) pp. 83–90.

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## Abstract

We consider random Cayley digraphs of order *n* with uniformly distributed generating sets of size *k*. Specifically, we are interested in the asymptotics of the probability that such a Cayley digraph has diameter two as *n* → ∞ and *k* = *f (n)*, focusing on the functions *f (n)* = ⌊*n*^{δ}⌋ and *f(n)* = ⌊cn⌋. In both instances we show that this probability converges to 1 as *n* → ∞ for arbitrary fixed *δ* ∈ (½, 1) and *c* ∈ (0,½), respectively, with a much larger convergence rate in the second case and with sharper results for Abelian groups.

Item Type: | Journal Item |
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Copyright Holders: | 2012 Discrete Mathematics and Theoretical Computer Science (DMTCS), Nancy, France |

ISSN: | 1365-8050 |

Keywords: | random digraph; Cayley digraph; degree; diameter |

Academic Unit/School: | Faculty of Science, Technology, Engineering and Mathematics (STEM) > Mathematics and Statistics Faculty of Science, Technology, Engineering and Mathematics (STEM) |

Item ID: | 41748 |

Depositing User: | Jozef Širáň |

Date Deposited: | 10 Feb 2015 17:07 |

Last Modified: | 07 Dec 2018 10:28 |

URI: | http://oro.open.ac.uk/id/eprint/41748 |

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