Vol 19 No 4 (2025): BAREKENG: Journal of Mathematics and Its Application
Articles

CERTAIN INDEXES OF UNIT GRAPH IN INTEGER MODULO RINGS WITH SPECIFIC ORDERS

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  • Sahin Two Lestari,
  • Jimboy R. Albaracin,
  • I Gede Adhitya Wisnu Wardhana
Sahin Two Lestari
Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas of Mataram, Indonesia
Jimboy R. Albaracin
Mathematics Program, College of Science, University of The Philippines Cebu, Gorordo Avenue, Philippines
I Gede Adhitya Wisnu Wardhana
Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas of Mataram, Indonesia
DOI: https://doi.org/10.30598/barekengvol19iss4pp2455-2466
Published September 1, 2025
Keywords
  • Harary Index,
  • Randic Index,
  • Schultz Index,
  • Unit Graph,
  • Wiener Index,
  • Zagreb Index
    • ...More
    Less
How to Cite
[1]
S. T. Lestari, J. R. Albaracin, and I. G. A. Wisnu Wardhana, “CERTAIN INDEXES OF UNIT GRAPH IN INTEGER MODULO RINGS WITH SPECIFIC ORDERS”, BAREKENG: J. Math. & App., vol. 19, no. 4, pp. 2455-2466, Sep. 2025.

Copyright (c) 2025 Sahin Two Lestari, Jimboy R. Albaracin, I Gede Adhitya Wisnu Wardhana

Creative Commons License

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Abstract

Topological indices quantify structural properties of graphs and find wide applications in chemistry, physics, and network analysis. This study investigates several key indices—namely the Harary Index, Wiener Index, Randić Index, Schultz Index, and the Zagreb Indices—within the context of unit graphs derived from the ring of integers modulo. General formulas for these indices are established, demonstrating how they reflect the combinatorial and algebraic characteristics of unit graphs. Each index captures distinct structural aspects: the Wiener Index evaluates global connectivity and correlates with molecular stability and boiling points; the Randić Index highlights molecular branching relevant to enzyme activity; the Harary Index models electronic interactions through distance reciprocals; and the Zagreb Indices and Schultz Index provide insights into bonding properties and molecular interactions. By linking these indices to unit graphs, this work reinforces the synergy between graph theory and algebra, offering a systematic framework to interpret algebraic structures through graph-based invariants. The results not only contribute to theoretical understanding but also suggest potential applications in modeling chemical compounds and complex networks, paving the way for further exploration of topological indices in other algebraically defined graphs.

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