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

Year 2025, Early Access, 1 - 14

Rauf Irshad , Maqsood Ahmad , Muhammad Hussain

https://doi.org/10.15672/hujms.1509270

Abstract

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.

Keywords

Atom Bond Connectivity index , Extremal graph; , Networks; , Graph invariants; , Transformed graphs; , Complete Graph

References

• [1] A. Ali and D. Dimitrov, On the extremal graphs with respect to bond incident degree indices, Disc. Appl. Math. 238, 32-40, 2018.