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Abstract:
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Regular two-graphs are antipodal distance-regular double coverings of the
complete graph, and they have many interesting combinatorial properties.
We derive a construction for regular two-graphs containing cliques of specified
order from their connection to large sets of equiangular lines in Euclidean
space. It is shown that the existence of a regular two-graph with
least eigenvalue ¿ containing a clique of order d depends on the existence of
an incidence structure on d points with special properties. Quasi-symmetric
designs provide examples of these incidence structures. |