Abstract
Given a finite abstract group G \mathcal {G} , whenever n n is sufficiently large there exist graphs with n n vertices and automorphism group isomorphic to G \mathcal {G} . Let ( G , n ) (\mathcal {G},n) denote the minimum number of edges possible in such a graph. It is shown that for each G \mathcal {G} there always exists a graph M M such that for n n sufficiently large, e ( G , n ) e(\mathcal {G},n) is attained by adding to M M a standard maximal component asymmetric forest. A characterization of the graph M M is given, a formula for e ( G , n ) e(\mathcal {G},n) is obtained (for large n n ), and the minimum edge problem is re-examined in the light of these results.
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