The number of certain dendrites of order three (Q1113483)

A dendrite is a Peano continuum with no simple closed curves. Let X be a dendrite with more than one point and let \(x\in X\). The rank of x in X, denoted Rank(x,X), is the number of components of \(X\setminus \{x\}\) and x is said to be a branch point if \(Rank(x,X)>2\). A dendrite X is defined to be a B-finite dendrite if it has only finitely many branch points and its order is defined to be the greatest of these ranks. The author determines, up to homeomorphism, the number of B-finite dendrites X of order three which have the property that for each branch point \(b\in X\), the closure of one of the three components of \(X\setminus \{b\}\) is either an arc or a triod.