Effect of atom bond connectivity index on family of graphs under transformation

Abstract

The atom-bond connectivity ($ABC$) index is a well-studied degree-related topological index that investigates the physicochemical properties of chemical compounds. It is a suitable predictor of stability and the strain energy of alkanes and cycloalkanes, respectively. In this work, first, we identify vertices for different families of $n$-vertex network with complete graphs of any order to obtain a new transformation network. Analogously, we get a variety of transformed graphs. Later, we compute the $ABC$ index for the transformed graphs acquired by the above-described process. The results thus obtained help us provide the extremal results regarding the $ABC$ index for the transformation graphs under discussion. Finally, we worked out several examples to check the accuracy of our results.

Keywords

• atom bond connectivity index
• extremal graph
• networks
• graph invariants
• transformed graphs
• complete graph

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