Analysis of Topological Indices in Unit Graphs of Modular Integer Rings

Authors

  • Ashadul Umam Department of Mathematics, Universitas Mataram
  • Abdul Gazir Syarifudin Department of Mathematics, Universitas Kebangsaan Republik Indonesia
  • Erma Suwastika Department of Mathematics, Institut Teknologi Bandung
  • I Gede Adhitya Wisnu Wardhana Department of Mathematics, Universitas Mataram

Keywords:

Narumi-Katayama index, Forgotten index, ABC index, Gourava index, Revan index

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.

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Published

2026-03-09

How to Cite

Umam, A., Syarifudin, A. G., Suwastika, E., & Wardhana, I. G. A. W. (2026). Analysis of Topological Indices in Unit Graphs of Modular Integer Rings. EIGEN MATHEMATICS JOURNAL, 9(1), 19–31. Retrieved from https://eigen.unram.ac.id/index.php/eigen/article/view/306

Issue

Vol. 9 No. 1 (2026): June

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