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All Journal Journal of Fundamental Mathematics and Applications (JFMA)
Lia Fitta Pratiwi
Department of Mathematics, University of Mataram
Decision Sciences, Operations Research & Management

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Estrada Index and Laplacian Estrada Index on the Non-Coprime Graph of the Dihedral Group of Prime PowerOrder Lia Fitta Pratiwi; I Gede Adhitya Wisnu Wardhana; Nur Idayu Alimon
Journal of Fundamental Mathematics and Applications (JFMA) Vol 9, No 1 (2026)
Publisher : Diponegoro University

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.14710/jfma.v9i1.26765

Abstract

Graphical representations of algebraic structures have become an important tool in modern mathematics and its applications. Graph theory, particularly spectral graph theory, is widely used across disciplines such as chemistry, physics, computer science, and network analysis to study structural and functional relationships. This study focuses on the non-coprime graph of the dihedral group \( D_{2n} \) with \(n=p^k \), where $p$ is a prime number, and \(k \in \mathbb{Z}^{+}\), analyzing two fundamental spectral parameters: the Estrada index and the Laplacian Estrada index, which are defined based on the eigenvalues of the graph’s adjacency and Laplacian matrices. The main result of this research is the derivation of explicit general formulas for both indices on the non-coprime graph of the dihedral group, contributing to the advancement of algebraic graph theory through spectral analysis.
Co-Authors I Gede Adhitya Wisnu Wardhana Nur Idayu Alimon