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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.

Analisis Pola Periodik Harga Saham Coca-Cola Menggunakan Deret Fourier dalam Model Regresi Linear Karang, Gusti Yogananda; Hardi, Rida Alkausar; Rizki, Miptahul; Robbaniyyah, Nuzla Af'idatur; Rusadi, Tri Maryono
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.v2i1.271

This study aims to identify periodic patterns and predict the movement of Coca-Cola (KO) stock prices using Fourier series in a linear regression model. The data utilized includes daily closing stock prices over the 2014-2024 period. A Fourier model with 15 harmonic components was chosen to optimize the balance between prediction accuracy and the risk of overfitting. The analysis results showed an R-squared value of 0.9174, indicating a high capability of capturing stock price variations. The detected price fluctuations reveal significant seasonal cycles and periodic trends. The price forecast for the 2024-2029 period indicates potential higher volatility, influenced by consumer demand dynamics, global economic uncertainty, product innovation, as well as geopolitical factors and climate change. These findings provide insights for investors to develop investment strategies based on the detected stock price fluctuation patterns.

Energy and Degree Sum Energy of Non-coprime Graphs on Dihedral Groups Karang, Gusti Yogananda; Wardhana, I Gede Adhitya Wisnu; Alimon, Nur Idayu; Sarmin, Nor Haniza
Journal of the Indonesian Mathematical Society Vol. 31 No. 1 (2025): MARCH
Publisher : IndoMS

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.22342/jims.v31i1.1900

Research on graphs has increasingly garnered attention in recent years.This research focuses on graph representations, with particular emphasis on non-coprime graphs within the dihedral group D_{2n} with n = p^k, prime numbers, $k \in \mathbb{Z}^+$. The non-coprime graph of a group G is defined as a graph in which the vertex set is G \{e}, and two distinct vertices r and s are connected by an edge if gcd(|r|,|s|) =\= 1. Specifically, this research examines the adjacency matrix energy and the degree sum energy of non-coprime graphs on dihedral groups. With the extensive application of chemical topological graphs in the field of chemistry, it is hoped that they can assist in the numerical analysis of chemical compounds used in healthcare, such as the analysis of vaccines for the COVID-19 epidemic.

Numerical Invariants Of Nilpotent Graphs In Integer Modulo Rings Malik, Deny Putra; Karang, Gusti Yogananda; Aini, Qurratul; Maulana, Fariz; Satriyantara, Rio
Contemporary Mathematics and Applications (ConMathA) Vol. 7 No. 2 (2025)
Publisher : Universitas Airlangga

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.20473/conmatha.v7i2.69650

Graph theory offers a robust framework for examining algebraic structures, especially rings and their elements. This paper focuses on the nilpotent graph of rings of the form Zpk, where p is a prime and k∈N, investigating both their structural and numerical properties. We begin by characterizing the nilpotent elements in these rings and examining their relationship to ring ideals. The study then presents theoretical results on key graph invariants, including connectivity, chromatic number, clique number, and specific subgraph configurations. To complement these, we also analyze numerical invariants such as edge count and degree distribution, which reveal deeper connections between ring-theoretic and graph-theoretic properties. Our results highlight consistent structural patterns in nilpotent graphs of Zpk and provide a concrete contribution to algebraic graph theory by bridging properties of commutative rings and their associated graphs.

ENERGY OF NON-COPRIME GRAPH ON MODULO GROUP Karang, Gusti Yogananda; Wisnu Wardhana, I Gede Adhitya; Angamuthu, Manimaran
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/barekengvol19iss4pp2937-2952

A graph is a mathematical structure consisting of a non-empty set of vertices and a set of edges connecting these vertices. In recent years, extensive research on graphs has been conducted, with one of the intriguing topics being the representation of graphs within algebraic structures, particularly groups. This approach bridges two areas of mathematics: graph theory and algebra. This study focuses on graph representation, specifically non-coprime graphs in the group of integers modulo , where , is a prime number, and is a non-negative integer. The non-coprime graph of a group is defined as a graph with the vertex set , where is the identity element of . Two distinct vertices and are connected by an edge if . Specifically, this research investigates the Sombor energy, the Degree Sum energy, the Degree Exponent Sum energy, the Laplacian energy, the Distance Laplacian energy, and the Distance Signless Laplacian energy of a non-coprime graph on a modulo group.

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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