Minimum atom-bond sum-connectivity index of unicyclic graphs with maximum degree

Abstract

Let G be a graph with edge set E ( G ) . Denote by d u the degree of a vertex u in G . The atom-bond sum-connectivity (ABS) index of G is defined as ABS ( G ) = (cid:80) xy ∈ E ( G ) (cid:112) ( d x + d y − 2) / ( d x + d y ) . In this article, we determine the minimum possible value of the ABS index of unicyclic graphs of order n and maximum degree ∆ such that 3 ≤ ∆ ≤ n − 2 . All the graphs that attain the obtained minimum value are also characterized.