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The Asymptotic Number of Labeled Graphs withnVertices,qEdges, and No Isolated Vertices

✍ Scribed by Edward A Bender; E Rodney Canfield; Brendan D McKay


Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
416 KB
Volume
80
Category
Article
ISSN
0097-3165

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✦ Synopsis


Let d(n, q) be the number of labeled graphs with n vertices, q N=( n 2 ) edges, and no isolated vertices. Let x=qÂn and k=2q&n. We determine functions w k t1, a(x), and .(x) such that d(n, q)tw k ( N q ) e n.(x)+a(x) uniformly for all n and q>nÂ2.

1997 Academic Press c(n, q)=u k \ N q + F(x) n A(x)(1+o(1)),