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All Journal Journal of the Indonesian Mathematical Society BAREKENG: Jurnal Ilmu Matematika dan Terapan JTAM (Jurnal Teori dan Aplikasi Matematika) EIGEN MATHEMATICS JOURNAL
Suwastika, Erma
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Computer Science & IT Control & Systems Engineering Economics, Econometrics & Finance Energy Engineering Mathematics Mechanical Engineering Physics Transportation

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Journal : EIGEN MATHEMATICS JOURNAL

 1 
A Novel Approach to Topological Indices of the Power Graph Associated with the Dihedral Group of a Certain Order Syarifudin, Abdul Gazir; Santi, Laila Maya; Shaumi, Nurina Fadlila; Suwastika, Erma; Wardhana, I Gede Adhitya Wisnu
Eigen Mathematics Journal Vol 8 No 2 (2025): December
Publisher : University of Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.29303/emj.v8i2.253

Abstract

Power graph of a group G, represented by \Gamma_G, is a graph where the vertex set consists of the elements of G. Two distinct vertices a, b \in G are connected by an edge if and only if there exists a positive integer m such that a^m = b or b^m = a. This study explores the utilization of a new approach to compute the topological indices of power graph associated with dihedral group with n=p^k, p is primes and k \in \mathbb{Z}. Results obtained indicate that the topological indices calculated using new approach yield the same values as those obtained with the conventional approach.
Analysis of Topological Indices in Unit Graphs of Modular Integer Rings Umam, Ashadul; Syarifudin, Abdul Gazir; Suwastika, Erma; Wardhana, I Gede Adhitya Wisnu
Eigen Mathematics Journal Vol 9 No 1 (2026): June
Publisher : University of Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.29303/emj.v9i1.306

Abstract

Topological indices are numerical graph invariants that reflect structural properties of graphs and have broad applications in chemistry, algebra, and network analysis. This paper focuses on the analysis of several topological indices in the context of unit graphs associated with modular integer rings. In a unit graph, vertices represent ring elements, and two vertices are adjacent if their sum is a unit. We investigate and derive general formulas for six indices: the Narumi-Katayama index, the Forgotten index, the Atom-Bond Connectivity (ABC) index, the first and second Gourava indices, and the first Revan index. Two cases are considered for the ring of integers modulo $n$, namely when $n$ is a power of $2$ and when $n$ is an odd prime. The results offer a deeper understanding of the algebraic and combinatorial properties of unit graphs and contribute to the development of algebraic graph theory.
Co-Authors Abrar, Ahmad Muchlas Faradiyah, Andi Rafiqa I Gede Adhitya Wisnu Wardhana Intan Muchtadi Alamsyah Rian Kurnia Santi, Laila Maya Shaumi, Nurina Fadlila Supu, Nur Ain Umam, Ashadul Wijaya, Verrel Rievaldo