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On k-connectivity for a geometric random graph

✍ Scribed by Mathew D. Penrose

Publisher: John Wiley and Sons
Year: 1999
Tongue: English
Weight: 255 KB
Volume: 15
Category: Article
ISSN: 1042-9832
DOI: 10.1002/(sici)1098-2418(199909)15:2<145::aid-rsa2>3.0.co;2-g

No coin nor oath required. For personal study only.

✦ Synopsis

For n points uniformly randomly distributed on the unit cube in d dimensions,

Ž

. with dG 2, let respectively, denote the minimum r at which the graph, obtained by n n adding an edge between each pair of points distant at most r apart, is k-connected Ž . w x respectively, has minimum degree k . Then P s ª 1 as n ª ϱ.

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