Effect of Atom Bond Connectivity index on family of Graphs under Transformation

Graph theory is an effective tool for modeling and devising an integrated system through a network. The nodes of the system behave as the vertices, and the connections amongst them behave as the edges of the graph representing the system under consideration. The graph is the best manifestation of the system by depicting it as a topological structure. The most studied graph invariant is the atom-bond connectivity index to identify and investigate the topological aspects of interconnection networks. In this work, firstly, we identify vertices for different families of n-vertex networks with complete graphs of any order to obtain a new transformation network. Analogously, we get a variety of transformed graphs. Finally, we provide the extremal results regarding the ABC index for the transformation graphs under discussion.