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This is a Quantitative Study study.

October 13, 2025Open Access

Relation of ABC and ABSC Index of Regular Graphs with Its Graph Operations

Key Points

The study computes the atom-bond connectivity index and ABSC index for various graph operations, enhancing understanding in graph theory.
Key results indicate the relationship of ABC and ABSC indices in regular graphs through operations like m-splitting and corona products.
The research introduces new methodologies for calculating both indices, demonstrating their importance in chemical property predictions.
Implications of this work may expand applications of graph indices in assessing molecular structures and their properties.

Abstract

Let G (V, E) be a simple connected graph of order n and size m. The Atom-Bond Connectivity (ABC) index \ (A B C (G) =ₔ ₕ ₄ (₆) dᵤ+dᵥ-2{dᵤ dᵥ}\) was introduced and developed by Cuban mathematician Ernesto Estrada for predicting chemical properties of molecular structures. The atom-bond sum-connectivity (ABSC) index \ (A B C (G) =ₔ ₕ ₄ (₆) dᵤ+dᵥ-2{dᵤ + dᵥ}\) is a recent topological index, first introduced in 2022 by amalgamating the atom-bond connectivity (ABC) index with the sum-connectivity index (SC). In this study, we establish some results which give the ABC and ABSC indices of graphs obtained by operations on regular graphs like construction by m-splitting, middle graph, subdivision and corona product.

Relation of ABC and ABSC Index of Regular Graphs with Its Graph Operations

Key Points

Abstract

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