A new sum of graphs and caterpillar trees

Abstract

Caterpillar trees, or simply Caterpillar, are trees such that when we remove all their leaves (or end edge) we obtain a path. The number of nonisomorphic caterpillars with n ≥ 2 edges is 2n−3 + 2⌊(n−3)/2⌋. Using a new sum of graphs, introduced in this paper, we provided a new proof of this result.