Asymptotic Enumeration of Combinatorial Structures.
Final technical rept.,
ABERDEEN UNIV (SCOTLAND)
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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-12. 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
- Statistics and Probability