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All Journal CAUCHY: Jurnal Matematika Murni dan Aplikasi BAREKENG: Jurnal Ilmu Matematika dan Terapan EIGEN MATHEMATICS JOURNAL Jurnal Diferensial Jurnal Pengabdian Inovasi Masyarakat Indonesia
Lestari, Sahin Two
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Agriculture, Biological Sciences & Forestry Chemistry Computer Science & IT Control & Systems Engineering Decision Sciences, Operations Research & Management Economics, Econometrics & Finance Education Energy Engineering Mathematics Mechanical Engineering Physics Public Health Social Sciences Transportation Other

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The First Zagreb Index, The Wiener Index, and The Gutman Index of The Power of Dihedral Group Asmarani, Evi Yuniartika; Lestari, Sahin Two; Purnamasari, Dara; Syarifudin, Abdul Gazir; Salwa, Salwa; Wardhana, I Gede Adhitya Wisnu
CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 7, No 4 (2023): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI
Publisher : Mathematics Department, Universitas Islam Negeri Maulana Malik Ibrahim Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.18860/ca.v7i4.16991

Abstract

Research on graphs combined with groups is an interesting topic in the field of combinatoric algebra where graphs are used to represent a group. One type of graph representation of a group is a power graph. A power graph of the group G is defined as a graph whose vertex set is all elements of G and two distinct vertices a and b are adjacent if and only if  or  for a positive integer  and . In addition to mathematics, graph theory can be applied to various fields of science, one of which is chemistry, which is related to topological indices. In this study, the topological indexes will be discussed, namely the Zagreb index, the Wiener index, and the Gutman index of the power graph of the dihedral group  where  with  prime numbers and an  natural number. The method used in this research is a literature review. The results obtained from this study are the first Zagreb index, Wiener index, and Gutman index of the power graph of the dihedral group  where  where  is prime and an m natural number respectively is .
Algebraic Structures and Combinatorial Properties of Unit Graphs in Rings of Integer Modulo with Specific Orders Lestari, Sahin Two; Dewi, Putu Kartika; Wardhana, I Gede Adhitya Wisnu; Suparta, I Nengah
Eigen Mathematics Journal Vol 7 No 2 (2024): December
Publisher : University of Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.29303/emj.v7i2.235

Abstract

Unit graph is the intersection of graph theory and algebraic structure, which can be seen from the unit graph representing the ring modulo n in graph form. Let R be a ring with nonzero identity. The unit graph of R, denoted by G(R), has its set of vertices equal to the set of all elements of R; distinct vertices x and y are adjacent if and only if x + y is a unit of R. In this study, the unit graph, which is in the ring of integers modulo n, denoted by G(Zn). It turns out when n is 2^k, G(Zn) forms a complete bipartite graph for k∈N, whereas when n is prime, G(Zn) forms a complete (n+1)/2-partites graph. Additionally, the numerical invariants of the graph G(Zn), such as degree, chromatic number, clique number, radius, diameter, domination number, and independence number complement the characteristics of G(Zn) for further research.
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.
TOPOLOGY INDEX OF THE COPRIME GRAPH FOR DIHEDRAL GROUP OF PRIME POWER ORDER Gayatri, Marena Rahayu; Fadhilah, Rifdah; Lestari, Sahin Two; Pratiwi, Lia Fitta; Abdurahim, Abdurahim; Wardhana, I Gede Adhitya Wisnu
JURNAL DIFERENSIAL Vol 5 No 2 (2023): November 2023
Publisher : Program Studi Matematika, Universitas Nusa Cendana

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.35508/jd.v5i2.12462

Abstract

In the field of molecular chemistry, graph theory is utilized to represent the structure of a molecule, where the set of nodes corresponds to its chemical elements and the set of edges represents the bonds within the chemical molecule. Graph theory, a mathematical discipline, finds application in various domains, one of which is group representation. This research will delve into the topic of the topological indices of the coprime graph of dihedral groups. The methodology employed involves reviewing several references related to dihedral groups, coprime graphs, and topological indices. This study yields results in the form of Harmonic index, Harary index, first Zagreb index, Gutman index, and Wiener index.
Pengenalan Algoritma Dengan Menggunakan Permainan Squaring the Square di SMA 1 Batukliang Utara Lombok Tengah Siboro, Ayes Malona; Wahidah, Fathul Maulina; Putra, Lalu Riski Wirendra; Lestari, Sahin Two; Putri, Syaftirridho; Pratama, Rendi Bahtiar; Haryati, Ida; Wardhana, I Gede Adhitya Wisnu
Jurnal Pengabdian Inovasi Masyarakat Indonesia Vol. 3 No. 2 (2024): Edisi Agustus
Publisher : Program Studi Pendidikan Kimia FKIP Universitas Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.29303/jpimi.v3i2.5326

Abstract

This study aims to evaluate the application of the Squaring Square method in improving the understanding of algorithms, geometry and changes in students' attitudes towards mathematics at SMA Negeri 1 Batukliang Utara, Central Lombok. This method involves practical activities in which students compose several small squares into one large square shape, designed to hone spatial skills and problem-solving abilities. Data analysis from the pre-test and post-test showed that applying this method significantly improved students' understanding of geometry concepts and their attitudes towards mathematics lessons. These findings align with constructivist theory, which emphasises the importance of experiential learning and visualization in improving deep conceptual understanding and offers valuable insights for teaching mathematics in schools.
Co-Authors Abdurahim, Abdurahim Albaracin, Jimboy R. Asmarani, Evi Yuniartika Dewi, Putu Kartika Fadhilah, Rifdah Gayatri, Marena Rahayu Haryati, Ida I Gede Adhitya Wisnu Wardhana Pratama, Rendi Bahtiar Pratiwi, Lia Fitta Prof. Dr.I Nengah Suparta,M.Si . Purnamasari, Dara Putra, Lalu Riski Wirendra Putri, Syaftirridho Salwa Salwa Siboro, Ayes Malona Wahidah, Fathul Maulina