On the Number of Continua Having a Finite Set of Non-cut Points

A continuum with finitely many non-cut points is an irreducible tree. A two-variable power series for the number of (unlabelled) irreducible trees with \(p\) pendant and \(q\) interior vertices.


The result is then specialized to get Harary's series for the number of irreducible trees with \(n\) vertices and to another series for the number of irreducible trees with \(p\) pendant vertices, a result of interest in continuum theory.