The asymptotic number of labeled graphswithn vertices , q edges , and no isolated
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چکیده
Let d(n; q) be the number of labeled graphs with n vertices, q N = ? n 2 edges, and no isolated vertices. Let x = q=n and k = 2q ?n. We determine functions w k 1, a(x), and '(x) such that d(n; q) w k ? N q e n'(x)+a(x) uniformly for all n and q > n=2.
منابع مشابه
The Asymptotic Number of Labeled Graphs withnVertices, qEdges, and No Isolated Vertices
Let d(n; q) be the number of labeled graphs with n vertices, q N = n 2 edges, and no isolated vertices. Let x = q=n and k = 2q n. We determine functions wk 1, a(x), and '(x) such that d(n; q) wk N q e uniformly for all n and q > n=2. Suggested Running Head: Graphs with no isolated vertices. Research supported by the National Security Agency.
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