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 \(A B C(G)=\sum_{u v \in E(G)} \sqrt{\frac{d_u+d_v-2}{d_u d_v}}\) was introduced and developed by Cuban mathematician Ernesto Estrada for predicting chemical properties of molecular structures. The atom-bond sum-connectivity (ABSC) index \(A B C(G)=\sum_{u v \in E(G)} \sqrt{\frac{d_u+d_v-2}{d_u + d_v}}\) 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.