ABERDEEN UNIV (Scotland)
Most widely held works by ABERDEEN UNIV (Scotland)
Enumeration of Large Combinatorial Structures ( Book )
4 editions published between 1975 and 1981 in English and held by 1 library worldwide
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 Temperley's 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.
Asymptotic Enumeration of Combinatorial Structures ( Book )
3 editions published between 1971 and 1973 in English and held by 1 library worldwide
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).
Problems in partition theory and related topics ( Book )
2 editions published between 1969 and 1970 in English and held by 1 library worldwide
Contents: Asymptotic relations between enumerative functions in graph theory; The number of graphs on many unlabelled nodes; Random graphs; The number of irreducible tournaments; Asymptotic enumeration of connected graphs; Graphs on many nodes with many edges; Coloured graphs.
Intelligence in a Democracy ( Book )
1 edition published in 1976 in English and held by 1 library worldwide
Asymptotic Problems in Graph Theory ( Book )
1 edition published in 1974 in English and held by 1 library worldwide
An (n, q) graph is one with n nodes and q edges. It is shown that the asymptotic probability that an (n, q) graph is Hamiltonian is the same whether it is labelled or unlabelled. Again the strict probability for the unlabelled case can decrease as q increases in a certain interval, but not for the labelled case. Dr. Sheehan and the author find a general formula for the number of Hamiltonian circuits in a thickly-edged graph; two very special cases of this were known. The use of the Exclusion-Inclusion Theorem to find asymptotic results can be extended more widely than had previously seemed possible. A detailed theory of the appearance of large cycles in large labelled graphs is developed. From this and other results there follows the somewhat paradoxical evolution of the unlabelled graph as the number of edges increases.
Partition of multipartite numbers into k parts ( Book )
1 edition published in 1941 in English and held by 1 library worldwide
Partitions of multipartites (i) and coloured graphs with a large number of nodes (ii) ( Book )
1 edition published in 1963 in English and held by 1 library worldwide
Structural chemistry of silicates and related substances ( Book )
1 edition published in 1960 in English and held by 1 library worldwide
Studies of oriented transformations, and crystal chemistry of oxides are described. Detailed study of the oriented transformations rhodonite to wollastonite provides direct evidence of the migration of Si during thermal transformations of silicates. The results of dry heating and hydrothermal treatment of a variety of other silicates are described. Crystal chemical studies, including a number of RO-R2O3 compounds are in progress. The stability relationships of the calcium gallates are described. (Author).