Abstract

Let H be an undirected simple graph with vertices vi,, v(k) and G(1),...,G(k) be a sequence formed with k disjoint graphs G(i) i = 1,, k. The H-generalized composition (or H-join) of this sequence is denoted by H [G(1),..,C-k]. In this work, we characterize the caterpillar graphs as a H -generalized composition and we study their spectra and Randic spectra, respectively. As an application, we obtain an improved and tight upper bound for the Energy and the Randic energy of these interesting trees.