A Survey on Progress and Perspectives on the Atom–Bond Sum Connectivity Index

LALITHA M; KIRUTHIKA P

A Survey on Progress and Perspectives on the Atom–Bond Sum Connectivity Index

Author(s)	Dr. LALITHA M, Ms KIRUTHIKA P
Country	India
Abstract	The Atom Bond Sum (ABS) index is a degree-based topological index that was introduced which has received much consideration in graph theory and network analysis because of its high ability to describe both structural and connectivity features in graphs. In contrast to conventional indices, the ABS index is able to represent the contribution of neighboring degrees of the vertex and thus it is applicable in the analysis of the extreme graphs, structural optimization, and predictive modeling. This study provides an overall overview of the ABS index including its mathematical expression, its theoretical features, and the end behavior of the index in significant classes of graphs including bipartite, cactus, and chordal graphs. Moreover, there is a discussion of algorithmic methods in extremal ABS detection such as the greedy techniques and the metaheuristic optimization. This study also investigates the ABS prediction in large and dynamic graphs by using Machine Learning (ML) and Deep Learning (DL) methods, including regression models, ensemble, or graph neural networks. Also under consideration are applications in chemical graph theory, network robustness assessment and structural optimization. Lastly, there are identified open challenges and gaps in the research, pointing to the future of scalable computation, dynamic graph analysis, and hybrid graph learning frameworks. This study gives a common base and guide to investigate the ABS based graph analysis and other network optimization issues.
Keywords	Atom–Bond Sum Index, Deep Learning, Extremal Graph Theory, Machine Learning, Topological Indices.
Field	Mathematics
Published In	Volume 8, Issue 1, January-February 2026
Published On	2026-02-17

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A Survey on Progress and Perspectives on the Atom–Bond Sum Connectivity Index

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