Abstract: The study of classification of subfactors was initiated by V.Jones, and has developed in the last 20 yrs, involving various different fields of mathematics, such as topology, mathematical physics. Many of the subfactors in fact come from some other mathematical objects, such as finite groups, quantum groups. Exotic subfactors are those who do not appear to come from those objects. U.Haagerup gave the list of the graphs that might be invariants for such subfactors, and proved that one of them is indeed the invariant of an exotic subfactor. In this talk I will discuss about an infinite sequence of parametrized graphs among the list and show that they are not invariants of a subfactor except for the first two. Classical algebraic number theory plays an unexpected role here.