Abstract The eccentric atom-bond sum-connectivity index (ABSC e) of a graph G is defined as A B S C e (G) = ∑ u v ∈ E (G) e u + e v − 2 e u + e v ABSC₄ (G) = ₔₕ ₄ (₆) {eₔ+{eₕ-2}{eₔ+eₕ}}, where e u and e v represent the eccentricities of u and v, respectively. In this paper, we investigate the eccentric atom-bond sum-connectivity index of trees and unicyclic graphs on n vertices with diameter d. We also characterize the extremal graphs.
Rui Song (Thu,) studied this question.