  For a countable ultrahomogeneous graph G let P(G) denote the collection of
domains of subgraphs of G isomorphic to G. The order types of maximal chains in
the set P(G) U {\o} ordered by the inclusion are characterized as:
  (I) the order types of compact sets of reals having the minimum non-isolated,
if G is the Rado graph or the Henson graph H_n, for some n>2;
  (II) the order types of compact nowhere dense sets of reals having the
minimum non-isolated, if G is the union of \mu disjoint complete graphs of size
\nu, where \mu \nu =\omega .
