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Abstract for Peter J. Cameron, Counting Two-graphs Related to Trees

In an earlier paper, I showed that the classes of
pentagon-free two-graphs and of pentagon-and-hexagon-free two-graphs
could be represented in terms of trees. This paper gives formulae for
the numbers of labelled objects in each of these classes, as well
as the numbers of labelled reduced two-graphs in each class. The proofs use
various enumeration results for trees. At least some of these
results are well-known. To make the paper self-contained,
I have included proofs.

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