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All Journal EIGEN MATHEMATICS JOURNAL Semeton Mathematics Journal Perspectives in Mathematics and Applications (PERMATA)
Umam, Ashadul
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Computer Science & IT Decision Sciences, Operations Research & Management Economics, Econometrics & Finance Engineering Mathematics Physics

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Journal : EIGEN MATHEMATICS JOURNAL

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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 Abdurahim, Abdurahim I Gede Adhitya Wisnu Wardhana Mifftahurrahman, Mifftahurrahman Pratiwi, Lia Fitta Suwastika, Erma