Enumeration of caterpillars

Abstract

Frank Harary and Allen J. Schwenk have given a formula for counting the number of non-isomorphic caterpillars on $n$ vertices with $n\ge 3$. Inspired by the formula of Frank Harary and Allen
J. Schwenk, in this paper, we give a formula for counting the number of non-isomorphic caterpillars with the same degree sequence.