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Jurnal Matematika UNAND
Published by Universitas Andalas
ISSN : 2303291X     EISSN : 27219410     DOI : -
Core Subject : Science, Education,
Computer Science & IT Mathematics
Fokus dan Lingkup dari Jurnal Matematika FMIPA Unand meliputi topik-topik dalam Matematika sebagai berikut : Analisis dan Geometri Aljabar Matematika Terapan Matematika Kombinatorika Statistika dan Teori Peluang.
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Articles 858 Documents
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ON THE EDGE METRIC DIMENSION OF HELM AND CLOSED HELM GRAPH Rahmadi, Deddy; Robiultsani, Muhammad Fauzi Nur; Abrori, Muchammad
Jurnal Matematika UNAND Vol. 14 No. 3 (2025)
Publisher : Departemen Matematika dan Sains Data FMIPA Universitas Andalas Padang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.25077/jmua.14.3.232-239.2025

Abstract

Dimensi metrik sisi merupakan kardinalitas himpunan pembeda pada suatu graf. Kumpulan verteks dikatakan himpunan pembeda jika untuk setiap verteks pada suatu graf, terdapat satu verteks yang membedakan setiap edge pada graf tersebut. Dengan kata lain, terdapat satu verteks dalam himpunan pembeda yang jaraknya berbeda terhadap setiap edge pada graf tersebut. Penelitian ini menggunakan metode pendekatan analisis struktur graf dan konsep jarak antara edge dan verteksnya untuk menentukan dimensi metrik sisi pada suatu graf. Graf helm $H_n$ dibangun dari graf roda $W_n$ dengan menambahkan satu verteks anting pada setiap verteks pada $n$ cycle. Graf helm tertutup $CH_n$ dibangun dari graf helm $H_n$ di mana pada setiap verteks antingnya membentuk sebuah cycle. Penelitian ini dapat memberikan landasan teoritis untuk menghitung dimensi metrik sisi pada graf helm dan graf helm tertutup. Diperoleh hasil dimensi metrik sisi pada graf helm $H_n$ untuk $n \geq 3$ dan graf helm tertutup $CH_n$ untuk $n \geq 3$.
ON ON THE PARTITION DIMENSION OF A SUBDIVISION OF COMPLETE GRAPH AND COMPLETE BIPARTITE GRAPH Hasibuan, Ismail Mulia; ABIDIN, WAHYUNI
Jurnal Matematika UNAND Vol. 14 No. 3 (2025)
Publisher : Departemen Matematika dan Sains Data FMIPA Universitas Andalas Padang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.25077/jmua.14.3.216-224.2025

Abstract

Let $G(V,E)$ be connected graph. The distance between two vertices $u,v\in V(G),$ denoted by $d(u,v),$ is the length of a shortest path from $u$ to $v$ in $G.$ The distance from a vertex $v\in V(G)$ to a set $S\subset V(G)$ is defined as $min\{d(v,x)|x\in S\}$. The partition $\Pi=\{S_{1},S_{2},...,S_{k}\}$ of $V(G)$ is called a resolving partition of $G$ if the vectors $(d(v,S_{1}),d(v,S_{2}),...,d(v,S_{k}))$ for all $v \in V(G)$ are distinct. The partition dimension of $G$, denoted by \emph{pd(G)}, is the smallest $k$ such that $G$ has a resolving $k$-partition. Let $A=\{e_1,e_2,...,e_t\}\subseteq E(G),$ for some $t$. The subdivision of a graph $G$ on the edge set $A,$ denoted by $S(G(A;n_1,n_2,...,n_t))$, is a graph obtained from the graph $G$ by replacing edge $e_1$ with a path of length $n_1+2,$ edge $e_2$ with a path of length $n_2+2,$ up to edge $e_t$ with a path of length $n_t+2,$ respectively. In this paper, we determine the partition dimension of $S(K_{n}(A;r_{1},r_{2}, \cdots, r_{t}))$ for $n\geq 3$ and $t\leq3$. We also derive that partition dimension of $S(K_{m,n}(A;r_{1},r_{2}, \cdots,r_{t}))$ for $m\geq n\geq 2$ and $t\leq3$
The THE LOCAL ANTIMAGIC TOTAL CHROMATIC NUMBERS ON BARBELL WHEEL GRAPHS Sugeng, Kiki A; M. Fachriza, Evan
Jurnal Matematika UNAND Vol. 14 No. 3 (2025)
Publisher : Departemen Matematika dan Sains Data FMIPA Universitas Andalas Padang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.25077/jmua.14.3.267-274.2025

Abstract

\textbf{Abstract}. % Dalam bahasa Inggris \textit{Let $G=(V,e)$ be a graph with a finite non-empty vertex set $V(G)$ and a edge set $E(G)$. A local antimagic total labeling on graph $G$ defined as a bijective mapping $f$ from a union of the vertex set and the edges set of $G$ to a set of integers $\{1,2,\dots,|V(G)|+|E(G)|\}$ such as for all two adjacent vertices $u$ and $v$ we have $w_t(u)\neq w_t(v)$, where $w_t(u)=f(u)+\sum_{e\in E(u)}{f(e)}$ is a weight of vertex $u$, and $E(u)$ is a set of adjacent edges on the vertex $u$. Each distinct vertex weight in local antimagic total labeling can be considered as distinct colors, so that local antimagic total labeling on graph $G$ induces vertex coloring on graph $G$, with minimum numbers of colors or its chromatic number denoted as $\chi_{lat}(G)$. The barbell wheel graph $BW_{n,k}$, with $n\geq3$ and $k\geq2$, is defined as a graph with two subgraphs of wheels $W_n$ that are connected by the path subgraph $P_k$ at each center vertex. In this paper, we prove that the barbell wheel graph $BW_{n,k}$ has local antimagic total labeling. We also determine its local antimagic total chromatic number.}\\
ON DETERMINING MANINJAU LAKE WATER QUALITY STATUS USING THE TSUKAMOTO AND MAMDANI METHODS DELLA, SEPTI RAHMA; NAZRA, ADMI; ARNAWA, I MADE
Jurnal Matematika UNAND Vol. 14 No. 4 (2025)
Publisher : Departemen Matematika dan Sains Data FMIPA Universitas Andalas Padang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.25077/jmua.14.4.424-438.2025

Abstract

Pada penelitian ini digunakan dua metode logika fuzzy, yaitumetode Tsukamoto dan metode Mamdani dalam membuat sebuah model penentuanstatus mutu air Danau Maninjau. Variabel input yang digunakan meliputisuhu air, pH, DO (Dissolved Oxygen), TSS (Total Suspended Solid), TDS (TotalDissolved Solid), BOD (Biochemical Oxygen Demand), COD (Chemical OxygenDemand), NO2, dan NO3 yang dibagi ke dalam dua kategori himpunan fuzzy, yaituAMAN dan TIDAK AMAN. Variabel output yaitu status mutu air yang dibagi ke dalamempat kategori himpunan fuzzy berdasarkan kriteria status mutu air, yaitu memenuhibaku mutu (MBM), cemar ringan (CR), cemar sedang (CS), dan cemar berat (CB).Hasil penelitian menunjukkan bahwa model status mutu air pada metode Tsukamotomenghasilkan nilai MAPE sebesar 40% dan nilai MSE 0,472, sedangkan pada metodeMamdani menghasilkan nilai MAPE sebesar 42% dan nilai MSE 0,678.
ON THE UPPERBOUND OF THE LOCATING CHROMATIC NUMBERS OF THE AMALGAMATION OF PATHS AND ITS BARBEL GRAPH AKMAL, AKMAL; Asmiati, Asmiati; NURYAMAN, AANG
Jurnal Matematika UNAND Vol. 14 No. 4 (2025)
Publisher : Departemen Matematika dan Sains Data FMIPA Universitas Andalas Padang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.25077/jmua.14.4.304-310.2025

Abstract

2002. Bilangan kromatik lokasi suatu graf merupakan perpaduan dari pewarnaan titik dan dimensi partisi graf\cite{C}. Misalkan $c$ suatu pewarnaan titik pada graf $G$ dengan $c(u)\ne c(v)$ untuk $u$ dan $v$  bertetangga di $G$. Misalkan $C_i$ himpunan titik-titik yang diberi warna $i$ dan $\Pi = \{C_1, C_2,\dots, C_k\}$ merupakan himpunan partisi dari $V(G)$. Kode warna $c_\Pi (v)$ dari $v$ adalah $k$-pasangan terurut $(d(v,C_1),d(v,C_2),\dots,d(v,C_k)$ dengan $d(v,C_i)=min\{d(v,x)|x\in C_i\}$ untuk $1\le i\le k$. Jika setiap titik di $G$ mempunyai kode warna yang berbeda, maka $c$ disebut pewarnaan lokasi dari $G$. Nilai terkecil $k$ sedemikian sehingga $G$ mempunyai pewarnaan lokasi disebut bilangan kromatik lokasi graf $G$. Amalgamasi dari $n\ge3$ buah graf lintasan $(P_m,m\ge3)$ dinotasikan dengan $_nP_m$  diperoleh dengan cara menyatukan satu titik dari setiap graf lintasan $P_m$. Graf barbel dari amalgamasi  lintasan diperoleh dengan menghubungkan dua jiplakan dari graf amalgamasi lintasan $_nP_m$, yang dihubungkan oleh sebuah sisi dinotasikan dengan $B(_nP_m )$. Batas atas bilangan kromatik lokasi graf amalgamasi lintasan untuk $m,n\ge3$ adalah $\lceil \sqrt{n} \ \rceil +1$ dan $\lceil \sqrt{n} \ \rceil +2$ untuk graf barbelnya.
(STRONG) RAINBOW CONNECTION NUMBERS ON CORONA PRODUCT OF PATH AND COMPLETE GRAPHS Sulistyanto, Andry; Halikin, Ikhsanul; Kusbudiono, Kusbudono; Wijaya, Kristiana
Jurnal Matematika UNAND Vol. 14 No. 4 (2025)
Publisher : Departemen Matematika dan Sains Data FMIPA Universitas Andalas Padang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.25077/jmua.14.4.376-389.2025

Abstract

Let G be an edge-colored, where adjacent edges may have the same color. A u-v path in G is a rainbow u-v path if no two edges of u-v path are colored the same. The graph G is called rainbow-connected if G contains a rainbow u-v path for every two vertices u and v of G. A rainbow connection number of rainbow-connected G is the minimum color in G. A rainbow u-v path is called a rainbow u-v geodesic if a rainbow u-v path of length distance from a vertex u to v. A graph G is strongly rainbow-connected if G contains a rainbow u-v geodesic for every two vertices u and v of G. The minimum color of the edges of G such that G is strongly rainbow-connected is the strong rainbow connection number. In this paper, we disccus (strong) rainbow connection number of corona product of path and complete graph. 
Stability Analysis and Traveling Wave Solutions of the Dynamic Model of Bird Flu Transmission in Poultry–Human Interaction Dilla, Rahma; Putri, Arrival Rince; Alfiany, Noverina; Syafwan, Mahdhivan
Jurnal Matematika UNAND Vol. 14 No. 4 (2025)
Publisher : Departemen Matematika dan Sains Data FMIPA Universitas Andalas Padang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.25077/jmua.14.4.355-365.2025

Abstract

This study analyzes the stability of a mathematical model of avian influenza virus spread in poultry-human interaction population. The analysis was conducted to see the dynamics of the spread of avian influenza virus. From the model, the equilibrium points and basic reproduction numbers associated with the stability of the system are obtained. The results obtained show that stability depends on the basic reproduction number. Numerical simulations were carried out using Maple and gave the result that the infection rate is low and the system reaches a stable state where the infection does not disappear but does not spread significantly.
ANALYSIS OF SOLVING THE BLACK-SCHOLES EQUATION USING THE FINITE DIFFERENCE METHOD WITH A NON-UNIFORM GRID Bulandari, Manisya; Syafwan, Mahdhivan; Asdi, Yudiantri
Jurnal Matematika UNAND Vol. 14 No. 4 (2025)
Publisher : Departemen Matematika dan Sains Data FMIPA Universitas Andalas Padang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.25077/jmua.14.4.451-462.2025

Abstract

Artikel ini mengimplementasikan metode beda hingga dengan skema eksplisit berbasis grid tidak seragam pada persamaan Black–Scholes untuk menghitung harga opsi call Eropa. Skema diturunkan menggunakan deret Taylor sehingga diperoleh sistem persamaan beda yang kemudian ditransformasikan ke dalam bentuk matriks dan diselesaikan secara rekursif melalui pemrograman Matlab. Berdasarkan simulasi numerik untuk nilai-nilai parameter tertentu, hasil yang diperoleh menunjukkan bahwa skema beda hingga dengan grid tidak seragam menghasilkan solusi yang lebih akurat dibandingkan grid seragam. Galat relatif lebih besar untuk harga saham yang berada di sekitar harga pelaksanaan, tetapi dapat dikurangi secara signifikan melalui penggunaan grid tidak seragam. Selain itu, pendekatan grid tidak seragam memberikan efisiensi komputasi yang lebih baik dibandingkan skema seragam.
Integral Hypergraphs Of The Cartesian Product Of Fano Plane And Latin Squares Of Order 3 Astuti, Mulia; Mayasari, Zulfia Memi; FAISAL, FACHRI; AFANDI, NUR
Jurnal Matematika UNAND Vol. 14 No. 4 (2025)
Publisher : Departemen Matematika dan Sains Data FMIPA Universitas Andalas Padang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.25077/jmua.14.4.333-340.2025

Abstract

Operasi pada hipergraf adalah suatu cara untuk mengkonstruksi suatu hipergraf dengan struktur yang lebih besar. Salah satu operasi pada hipergraf yang biasa dipelajari adalah operasi kali Kartesius. Suatu hipergraf dikatakan integral jika semua nilai karakteristik dari matriks ketetanggaannya adalah bilangan bulat. Dalam makalah ini, dipelajari dua kelas hipergraf yaitu, bidang Fano dan latin square orde 3. Dapat ditunjukkan bahwa kedua kelas hipergraf tersebut adalah integral. Selanjutnya, ditentukan hipergraf hasil operasi kali Kartesius dari kedua hipergraf tersebut. Dapat dibuktikan bahwa operasi kali Kartesius pada hipergraf mempertahankan sifat keintegralan.
Numerical Modelling of Social Media Addiction Cases Using 15th Order Runge-Kutta Fatahillah, Arif; Prihandini, Rafiantika Megahnia; Hidayatullah, Arfan; Setiawani, Susi; Adawiyah, Robiatul
Jurnal Matematika UNAND Vol. 14 No. 4 (2025)
Publisher : Departemen Matematika dan Sains Data FMIPA Universitas Andalas Padang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.25077/jmua.14.4.400-410.2025

Abstract

The advancement of information technology has led to more and more people, especially teenagers, becoming addicted to using various social platforms. Despite being a very useful application for social interaction, the habit of spending excessive time on social media is prone to addiction so that teenagers can experience anxiety disorders, depression, health problems, and more. The purpose of this study is to determine the effectiveness of the 15th-order Runge-Kutta method in solving mathematical models in the case of social media addiction. The method used in this research uses experimental research and data collection is done by systematically observing and recording the research indicators. The research was conducted by observing the error, number of iterations, running time, and graphs. In this study, adolescents aged 15-18 years were divided into three compartment states which were modeled into mathematical equations. The results of this study indicate that the 15th order Runge-Kutta method is more effective for solving mathematical models on social media addiction compared to Ordinary Differential Equation (ODE).

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