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All Journal Journal of the Indonesian Mathematical Society BAREKENG: Jurnal Ilmu Matematika dan Terapan
Albaracin, Jimboy R.
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Computer Science & IT Control & Systems Engineering Economics, Econometrics & Finance Energy Engineering Mathematics Mechanical Engineering Physics Transportation

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On Sombor Energy of the Nilpotent Graph of the Ring of Integers Modulo ε Putra, Lalu Riski Wirendra; Albaracin, Jimboy R.; Wardhana, I Gede Adhitya Wisnu
Journal of the Indonesian Mathematical Society Vol. 31 No. 3 (2025): SEPTEMBER
Publisher : IndoMS

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.22342/jims.v31i3.1856

Abstract

In chemical graph theory, chemical compounds are represented as graphs where atoms are represented as vertices, and the bonds connecting the atoms are represented as edges. In 2021, Gowtham and Swamy discovered another type of graph energy, called the Sombor energy. This discovery was motivated by Gutman's introduction of the Sombor index in the same year. In the field of abstract algebra, rings can also be represented as graphs. In this article, we aim to explore the Sombor energy of some nilpotent graphs of rings, particularly the ring of integers modulo ε.
CERTAIN INDEXES OF UNIT GRAPH IN INTEGER MODULO RINGS WITH SPECIFIC ORDERS Lestari, Sahin Two; Albaracin, Jimboy R.; Wisnu Wardhana, I Gede Adhitya
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 19 No 4 (2025): BAREKENG: Journal of Mathematics and Its Application
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol19iss4pp2455-2466

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.
Co-Authors I Gede Adhitya Wisnu Wardhana Lestari, Sahin Two Putra, Lalu Riski Wirendra