  The Galois group of the minimal polymonal of a Jones index value gives a new
type of obstruction to a principal graph, thanks to a recent result of
P.Etingof, D.Nikshych, and V.Ostrik. We show that the sequence of the graphs
given by Haagerup as candidates of principal graphs of subfactors, are not
realized as principal graphs for 7<n <= 27 using GAP program. We further
utilize Mathematica to extend the statement to 27 <n <= 55. We conjecture that
none of the graphs are principal graphs for all n>7, and give an evidence using
Mathematica for smaller graphs among them for n>55. The problem for the case
n=7 remains open, however, it is highly likely that it would be realized as a
principal graph, thanks to numerical computation by Ikeda.
