  Given a set D of nonnegative integers, we derive the asymptotic number of
graphs with a givenvnumber of vertices, edges, and such that the degree of
every vertex is in D. This generalizes existing results, such as the
enumeration of graphs with a given minimum degree, and establishes new ones,
such as the enumeration of Euler graphs, i.e. where all vertices have an even
degree. Those results are derived using analytic combinatorics.
