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

Let G be a graph with edge set E(G).Denote by du the degree of a vertex u in G.The atom-bond sum-connectivity (ABS) index of G is defined as ABS(G) = xy∈E(G) (dx + dy -2)/(dx + dy).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.