Enumeration of caterpillars

V. Murugan1, G. Sethuraman2
1Department of Mathematics, VIT, Vellore, India.
2Department of Mathematics, Anna University, Chennai, India

Abstract

Frank Harary and Allen J. Schwenk have given a formula for counting the number of non-isomorphic caterpillars on \(n\) vertices with \(n ≥ 3\). 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.

Keywords: Graph Enumeration, Tree isomorphism, Non-isomorphic caterpillars, Degree sequence