Enumeration of Large Combinatorial Structures.
Final technical rept. Dec 74-Nov 77,
ABERDEEN UNIV (SCOTLAND)
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New results are given about the number of 2-connected labelled n,q graphs, i.e. graphs on n points and q lines, including a combinatorial interpretation of Temperleys differential equation satisfied by the exponential generating function of this number applicable in Statistical Mechanics. This leads to two methods for finding asymptotic approximations to this number. A curious paradox is found in the asymptotic enumeration of unlabelled graphs. Work was continued on connected, sparsely-edged graphs of various kinds, again including asymptotic results with possible applications. Finally a new ghost expansion method is described to obtain asymptotic results from the Exclusion-Inclusion Theorem by applying the method to a particular graphical example. The appendices consist of four research papers which have been submitted for publication to different mathematical journals.
- Numerical Mathematics