Four different views of Glasgow University Tower
My research interests at the present time are in the area of
classification of combinatorial designs of various different sorts, including
Hadamard mareices, 2-designs, Two-graphs, strongly regular graphs and cospectral graphs.
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 links in the side-bar on the left . 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 .
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
All the results of  have now been extended to the case n =12. I have
completed the investigation for n = 12 and the
as well as the signless Laplace spectrum.
One further aspect considered 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 of the data for all these different spectra may be found by
accessing the appropriate link on the sidebar on the left-hand side of the page.
 A. E. Brouwer and E Spence, Cospectral graphs on 12 vertices, Elec.
Journ. Combin., Vol. 16 (20) (2009).
 W. H. Haemers, E. Spence, Enumeration of cospectral graphs, European
J. Combin, 25 (2004), 199-211.