Analysis of the ABC Index on Inverse and Non-Commuting Graphs of Finite Groups

Sefti Fajriatul Musyarrofah; Rio Satriyantara

Authors

Sefti Fajriatul Musyarrofah Universitas Mataram Author
Rio Satriyantara Universitas Mataram Author

Keywords:

Atom Bond-Connectivity, Invers Graph, Non-Commuting Graph, Finite Group, Topological Index

Abstract

This study investigates the Atom Bond Connectivity (ABC) index applied to inverse and non-commuting graphs of finite groups. The research focuses on two distinct structures: inverse graphs formed from generalized quaternion groups and non-commuting graphs derived from non-abelian finite groups. By utilizing topological index theory, particularly the ABC index introduced by Estrada, the study aims to characterize the graph structures based on vertex degrees. For the inverse graphs of generalized quaternion groups, the ABC index is determined using known group properties and edge classifications. Similarly, the ABC index of non-commuting graphs is explored by analyzing group centers and the connectivity patterns among non-central elements. The results reveal that the ABC index provides a meaningful quantification of group connectivity, enhancing the understanding of structural properties in algebraic graph representations. This analysis contributes to the broader application of graph theory in abstract algebra and theoretical chemistry.

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