Synopsis The number of different connected graphs (with some propertyP) onnlabelled nodes withqedges isfnq. AgainFnqis the number of graphs onnlabelled nodes withqedges, each of whose connected components has propertyP. We consider 8 types of graph for which . We use a known relation between the generating functions offnqandFnqto find an asymptotic expansion offnqin terms of binomial coefficients, valid if (q– ½nlogn)/n→∞ asn→∞. This condition is also necessary for the existence of an asymptotic expansion of this kind.
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E. M. Wright (1970) studied this question.
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