ScholarWorks@성균관대학교

초록

Recently, the atom-bond sum-connectivity index (denoted as ABS) was introduced as a novel topological index in chemical graph theory. The ABS index of a graph G is defined as (Formula Presented) where di represents the degree of the vertex vi in G. An important problem in discrete mathematics is the characterization of extremal structures concerning graph invariants within the class of bicyclic graphs. In this context, Ali et al. [Extremal results and bounds for the atom-bond sum-connectivity index, MATCH Commun. Math. Comput. Chem. 92 (2024) 271–314] proposed a conjecture regarding the characterization of bicyclic graphs that minimize the ABS index. This article fully characterizes the bicyclic graph that achieves the minimum ABS index, thereby resolving the conjecture.