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An asymptotic formula for the number of graphs having small diameter

✍ Scribed by Ioan Tomescu

Publisher: Elsevier Science
Year: 1996
Tongue: English
Weight: 351 KB
Volume: 156
Category: Article
ISSN: 0012-365X
DOI: 10.1016/0012-365x(94)00241-a

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✦ Synopsis

In this paper it is shown that for every fixed k 1> 3, G(n; d = k) = 2(~) (6.2 -k + o(1))", where G(n; d = k) denotes the number of graphs of order n and diameter equal to k. It is also proved that for every fixed k>~2, lim,~G(n;d=k)/G(n;d=k+ 1)=lim.o~G(n;d=n-k)/ G(n;d=n-k+ 1)= oo hold.

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