We describe a very general technique for generating families of combinatorial objects without isomorphs. It applies to almost any class of objects for which an inductive construction process exists.… Expand

Some new constructions for families of cospectral graphs are derived, and some old ones are considerably generalized. One of our new constructions is sufficiently powerful to produce an estimated 72%… Expand

The method used is a switching argument recently used by us to uniformly generate random graphs with given degree sequences to determine the asymptotic number of unlabelled graphs with a given degree sequence.Expand

Let c(n, q) be the number of connected labeled graphs with n vertices and q ≤ N = (2n) edges. Let x = q/n and k = q − n. We determine functions wk ˜ 1. a(x) and φ(x) such that c(n, q) ˜… Expand

We present the numbers of isotopy classes and main classes of Latin squares, and the numbers of isomorphism classes of quasigroups and loops, up to order 10. The best previous results were for Latin… Expand