On structural properties of ABC-minimal chemical trees

Abstract

The atom-bond connectivity (ABC) index of a connected graph G is defined as ABC(G)=∑uv∈E(G)d(u)+d(v)−2d(u)d(v), where d(w) is the degree of vertex w in G and E(G) is the set of edges of G. Given greedy trees perturbed by different degree sequences, we investigate the behaviors on their ABC index in this paper. Moreover, we also give the minimum ABC index and its structural properties of the chemical trees with n vertices and p pendant vertices for n≥3p−2.