On the maximum atom-bond sum-connectivity index of molecular trees

Abstract

Let G be a graph with V(G) and E(G), as vertex set and edge set, respectively. The atom-bond sum-connectivity (ABS) index is a vertex-based topological index which is defined as ABS ( G ) = ∑ ab ∈ E ( G ) ϱ a + ϱ b − 2 ϱ a + ϱ b , where ϱ a is the degree of the vertex a. In this paper, we obtain sharp upper bounds for the ABS index of molecular trees in terms of order and number of branching vertices and vertices of degree two.