In (I), hypertrees and uniform hypertrees are enumerated. Continuing the work of (I), the authors consider the problem of enumeration of hypertrees with constrains to extend Clarke's formula, Moon's formula, Temperley's formula, Weinberg's formula and O'Neil's formula of simple labeled trees to hypertrees.
Enumeration of labeled connected graphs with k cycles is an open problem . Up to now it has been settled only for k = 1, 2. Unfortunately , these given for-mulas are very complicated . In this paper we improve a series of enum nerations and solve the enumeration problem for k = 3.
