Asymptotic Enumeration of Combinatorial Structures.
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)
Document Details
- Document Type
- Technical Report
- Publication Date
- Sep 01, 1972
- Accession Number
- AD0751901
Entities
People
- E. M. Wright
Organizations
- University of Aberdeen