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

Abstract

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.