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Indeks Topologi Padmakar Ivan dan Szeged pada Graf Koprima Prima dari Grup Bilangan Bulat Modulo Abdurahim, Abdurahim; Pratiwi, Lia Fitta; Karang, Gusti Yogananda; Wardhana, I Gede Adhiya Wisnu; Irwansyah, Irwansyah; Awanis, Zatta Yumni; Romdhini, Mamika Ujianita
Square : Journal of Mathematics and Mathematics Education Vol. 6 No. 2 (2024)
Publisher : UIN Walisongo Semarang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.21580/square.2024.6.2.22836

The Prime Coprime Graph is defined as a graph in which two distinct vertices are adjacent if and only if the greatest common divisor of their orders is 1, indicating that they are coprime. This research focuses on deriving general formulas for the Padmakar-Ivan index and the Szeged index for the coprime prime graph of the modulo integer group with n=p^k, where p is a prime number and k is not less than 2. As a result of this study, explicit formulas for the Padmakar-Ivan and Szeged indices were obtained, along with an analysis of the relationship between these two indices.Keywords: prime coprime graph, Padmakar-Ivan index, Szeged index.

Eksplorasi Modul Noetherian Umam, Ashadul; Mifftahurrahman, Mifftahurrahman; Pratiwi, Lia Fitta
Semeton Mathematics Journal Vol 2 No 1 (2025): April
Publisher : Program Studi Matematika

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.29303/semeton.v2i1.263

Noetherian Modules are a fundamental concept in algebra, providing a structured framework for studying algebraic structures. These modules satisfy the ascending chain condition (ACC), which ensures that every ascending chain of submodules terminates after a finite number of steps. This article explores the definition, key properties, and applications of Noetherian modules in ring theory, homological algebra, and algebraic topology. Through this discussion, it is demonstrated that Noetherian Modules play a crucial role in analyzing ideal structures and more complex algebraic representations. The article also provides concrete examples to illustrate the properties and significance of Noetherian modules across various branches of algebra.

ABC Index Analysis: Physical Properties of Prenylated Xanthone Pratiwi, Lia Fitta; Mufarrihati, Ardelia; Dharmayani, Ni Komang Tri; Wardhana, I Gede Adhitya Wisnu
JURNAL DIFERENSIAL Vol 7 No 2 (2025): November 2025
Publisher : Program Studi Matematika, Universitas Nusa Cendana

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.35508/jd.v7i2.20418

Xanthone is a heterocyclic compound with various substituents (hydroxy, prenyl, geranyl, methoxy, halogens, and others). The presence of these substituents contributes to diverse biological activities, including anticancer, antidiabetic, and antioxidant properties. This study aims to optimize the design of xanthone derivatives through a mathematical approach using Chemical Topological Graphs (CTG) and the Atom-Bond Connectivity (ABC) index. A literature review was conducted to identify the physicochemical properties, biological activities, and molecular structures of compounds such as 1,7-dihydroxy-3-methoxy-2-(3-methylbut-2-enyl)xanthone (1), Gartanin (2), and Garcinon (3). These xanthone derivatives are distinguished by the number of prenyl substitutions on their core structures. Chemical graph theory is employed to represent molecular structures, with atoms represented as nodes and chemical bonds as edges. The ABC index is calculated based on the degree of connected atoms within the molecules and correlated with the compounds’ physicochemical properties and bioactivity. The ABC index values for compounds (1), (2), and (3) are 32.186, 43.987, and 51.744, respectively. These values indicate that an increase in prenyl substitutions leads to higher ABC index values, which correspond to decreased polarity, increased boiling points, and enhanced bioactivity and stability of the xanthone derivatives

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

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.

Indeks Topologi Padmakar Ivan dan Szeged pada Graf Koprima Prima dari Grup Bilangan Bulat Modulo Abdurahim, Abdurahim; Pratiwi, Lia Fitta; Karang, Gusti Yogananda; Wardhana, I Gede Adhiya Wisnu; Irwansyah, Irwansyah; Awanis, Zatta Yumni; Romdhini, Mamika Ujianita
Square : Journal of Mathematics and Mathematics Education Vol. 6 No. 2 (2024)
Publisher : UIN Walisongo Semarang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.21580/square.2024.6.2.22836

The Prime Coprime Graph is defined as a graph in which two distinct vertices are adjacent if and only if the greatest common divisor of their orders is 1, indicating that they are coprime. This research focuses on deriving general formulas for the Padmakar-Ivan index and the Szeged index for the coprime prime graph of the modulo integer group with n=p^k, where p is a prime number and k is not less than 2. As a result of this study, explicit formulas for the Padmakar-Ivan and Szeged indices were obtained, along with an analysis of the relationship between these two indices.Keywords: prime coprime graph, Padmakar-Ivan index, Szeged index.

Implementasi Modul Olimpiade SMP Di SMPN 2 Kuripan Lombok Barat Putra, Lalu Riski Wirendra; Pratama, Rendi Bahtiar; Karang, Gusti Yogananda; Irwansyah, Irwansyah; Wardhana, I Gede Adhitya Wisnu; Romdhini, Mamika Ujianita; Abdurahim, Abdurahim; Maulana, Fariz; Satriyantara, Rio; Awanis, Zata Yumni; Putri, Syaftirridho; Graha, Syifa Salsabila Satya; Wahidah, Fathul Maulina; Pratiwi, Lia Fitta; Pradana, Satriawan; Siboro, Ayes Malona; Farwan, Farwan
Sinergi dan Harmoni Masyarakat MIPA Vol. 1 No. 1 (2024): Oktober
Publisher : Fakultas Matematika dan Ilmu Pengetahuan Alam

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.29303/sinonim.v1i1.5517

Kegiatan pengabdian kepada masyarakat ini bertujuan untuk mengimpelementasikan modul pembelajaran olimpiade matematika bagi siswa SMPN 2 Kuripan. Kebutuhan akan modul ini didasarkan pada rendahnya akses siswa terhadap materi-materi persiapan olimpiade yang terstruktur dan sesuai dengan kemampuan serta kebutuhan mereka. Metode yang digunakan dalam pengembangan modul ini meliputi analisis kebutuhan, desain dan pengembangan modul, serta uji coba. Modul ini dirancang untuk mencakup berbagai topik matematika yang sering muncul dalam olimpiade, disertai dengan contoh soal dan pembahasan yang mendalam. Hasil dari kegiatan ini menunjukkan bahwa penggunaan modul olimpiade matematika ini dapat meningkatkan pemahaman siswa terhadap materi olimpiade, serta memotivasi mereka untuk lebih aktif dalam mengikuti kompetisi. Evaluasi melalui uji coba menunjukkan respon positif dari siswa, dengan peningkatan signifikan pada hasil latihan soal.

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