Sharp inequalities for the atom-bond sum-connectivity index of graph operations

The atom-bond sum-connectivity index of a graph G is defined as {equation*} ABSC(G)=∑uv∈ E(G)√d(u)+d(v)-2/d(u)+d(v)=∑uv∈ E(G)√1-2/d(u)+d(v) {equation*} where $d(u)$ and $d(v)$ represent the degrees of vertices u and v respectively. In this paper, we will determine the sharp upper and lower bounds for the atom-bond sum-connectivity index of a series of graph operations, including the addition (G+H), the Cartesian product(G× H), the composition (G[H]), and the corona product (GoH) of graphs, where G and H representing graphs. We also identify and describe the graphs that achieve extremal values.