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

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.