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Asymptotic Enumeration of Combinatorial Structures.

Author: E M Wright; ABERDEEN UNIV (Scotland)
Publisher: Ft. Belvoir Defense Technical Information Center SEP 1972.
Edition/Format:   Book : EnglishView all editions and formats
Database:WorldCat
Summary:
The report completes the solution of the problem of finding an asymptotic approximation to T, the number of unlabelled graphs on n nodes with q edges, for all large value of min (q, N-q) where N = n (n-1)/2. Improvement of the bound for the error term enables making applications. It is found that the limit as n approaches infinity of B the probability of a random (n, q) graph being connected. This result differs  Read more...
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Document Type: Book
All Authors / Contributors: E M Wright; ABERDEEN UNIV (Scotland)
OCLC Number: 227689366
Description: 56 p.

Abstract:

The report completes the solution of the problem of finding an asymptotic approximation to T, the number of unlabelled graphs on n nodes with q edges, for all large value of min (q, N-q) where N = n (n-1)/2. Improvement of the bound for the error term enables making applications. It is found that the limit as n approaches infinity of B the probability of a random (n, q) graph being connected. This result differs significantly from that found for labelled graphs. It is found and proven that for a certain range of q, the connectedness of B decreases as q increases. Announcement is made of a more exact result which depends on further refinements of the asymptotic results found for T. (Author).

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