My research interests at the present time are in the area of classification of combinatorial designs of various different sorts. In some cases I have been able to classify the designs completely and where this has been possible I have stored the designs on disc. They can be accessed via the Table below. These files will be updated at intervals, as I find the time.

Recently, along with Andries Brouwer, I have extended some of the results that Willem Haemers and I obtained concerning cospectral graphs, W. H. Haemers, E. Spence Enumeration of cospectral graphs, European J. Combin, 25 (2004), 199-211.

In that paper Haemers and I considered graphs with n <= 11 vertices and determined the number that were cospectral with respect to the usual graph spectrum, together with the number cospectral with respect the Laplace and unsigned Laplace spectrum. Moreover, we also found the number of graphs G, H for which both G and H are cospectral and also their complements. For details of the results for the usual spectrum and n <= 12 see Andries Brouwer's home page or files on this computer. So far I have completed the investigation for n = 12 and the signless Laplace spectrum. The results are listed here. The results for the Laplace spectrum can be found here.

One further aspect considered in the above paper is the question of the number of graphs G for which G and its complement G' have the same pair of characteristic polynomials, ( P, Q ) say. For graphs on less than seven vertices the answer is none. The details for graphs on n = 7, 8, 9, 10, 11 and 12 vertices may be found here .

If you do download any of my files, it would be appreciated if you would e-mail me a message to let me know that you have done so: ted@maths.gla.ac.uk

Department of Mathematics University of Glasgow Glasgow G12 8QQ SCOTLAND

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