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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 10 Documents
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Search results for , issue "Vol. 14 No. 3 (2025)" : 10 Documents clear
THE LOCATING-CHROMATIC NUMBER FOR CERTAIN BARBELL OPERATION ON PIZZA GRAPH AND ITS SUBDIVISION Irawan, Agus; Asmiati, Asmiati
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.14.3.293-303.2025

Abstract

In graph theory, the locating-chromatic number is a parameter that characterizes the minimum number of colors required to assign to the vertices of a graph such that each vertex can be uniquely identified by its color and the colors of its neighbors. The locating-chromatic number of a graph refers to a concept in graph coloring, which involves assigning colors to the vertices of a graph in such a way that adjacent vertices do not share the same color. It represents the minimum number of colors needed for a proper vertex coloring. This study investigates the locating-chromatic number of certain barbell operation on pizza graphs and its subdivisions
ZONAL LABELING OF VERTEX COMB PRODUCT OF GRAPHS Amruddin, Mustaqim; Haning, Farly Oktriany; Putra, Ganesha Lapenangga; Pahnael, Jusrry Rosalina
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.14.3.225-231.2025

Abstract

Suppose there is a connected plane graph G with a set of vertex V (G) and a set of edges E(G) or G = (V,E). A zonal labeling of graph G is vertex labeling with the two nonzero elements of ring Z3 to vertex in graph G such that the sum of the label of the vertices on the boundary of every region of G is the zero elements in Z3. This labeling is zonal and graph G is zonal graph. This paper will discuss zonal labeling on a graph comb product with a graph zonal denoted G. The result states that Fy ⊵o G, T ⊵o G, U ⊵o G a is graph zonal and Wz ⊵o G is not a zonal graph.
DINAMIKA INTERAKSI SISTEM IMUN TUBUH DAN MYCOBACTERIUM TUBERCULOSIS MENGGUNAKAN PERSAMAAN DIFERENSIAL FRAKSIONAL Rosita, Rosita; Adi, Yudi Ari
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.14.3.275-292.2025

Abstract

Tuberkulosis yang disebabkan oleh bakteri Mycobacterium tuberculosis (MTb) merupakan penyakit menular yang utamanya menyerang paru-paru dan masih menjadi penyebab kematian global. Artikel ini mengkaji dinamika interaksi antara sis tem imun tubuh dan bakteri MTb melalui model matematika yang berbentuk persamaan diferensial fraksional dengan mempertimbangkan pemberian vaksinasi. Model fraksional tipe Caputo-Fabrizio yang digunakan dalam model ini merepresentasikan efek memori dan ketergantungan temporal dalam respons imun, salah satu aspek yang penting dalam infeksi MTb. Selanjutnya dilakukan analisis kestabilan titik kesetimbangan dan sensi tivitas model, serta mensimulasikan dinamika sistem imun. Analisis dilakukan untuk menentukan kestabilan titik kesetimbangan dan pengaruh variasi orde fraksional ter hadap kecepatan konvergensi. Hasil menunjukkan adanya dua titik kesetimbangan: titik bebas infeksi yang stabil jika R0 < 1 dan titik infeksi yang stabil pada kondisi tertentu. Simulasi numerik memperlihatkan bahwa semakin kecil orde fraksional, semakin cepat respons sel imun menuju titik kestabilan, menunjukkan pengaruh signifikan dari param eter orde α terhadap kecepatan konvergensi. Temuan ini diharapkan dapat memberikan wawasan baru untuk pengendalian infeksi MTb secara lebih efektif melalui pendekatan model fraksional.
PELABELAN ANTI AJAIB PADA GRAF HASIL KALI SISIR Liunokas, Mariance Crisatya; Lapenangga Putra, Ganesha; Pangaribuan, Rapmaida Megawaty; Pasangka, Irvandi Gorby
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.14.3.240-252.2025

Abstract

Suatu graf $G$ dikatakan graf anti ajaib jika memuat pelabelan anti ajaib, yaitu $f : E(G) \rightarrow \{1,2,…, |E(G)|\}$ merupakan fungsi bijektif, dan untuk setiap simpul memiliki nilai bobot yang berbeda. Dalam tulisan ini, terdapat beberapa pelabelan anti ajaib dengan menggunakan operasi hasil kali sisir, dan hasilnya adalah graf $C_m \unrhd_o C_n, P_m \unrhd_o C_n, S_m \unrhd_o C_n, W_m \unrhd_o C_n$ dan secara umum untuk $G$ suatu graf terhubung dan $r-reguler$, $ G\unrhd_oC_n$ merupakan graf anti ajaib. A graph $G$ is said to be antimagic if it contains an antimagic label, that is, $f : E(G) \rightarrow \{1,2,…, |E(G)|\}$ is a bijective function, and each vertex has a different weight value. In this paper, there are several anti-magic labelings using the comb product operation and the results are the graphs $C_m \unrhd_o C_n, P_m \unrhd_o C_n, S_m \unrhd_o C_n, W_m \unrhd_o C_n$ and in general for $G$ a connected and $r-regular$ graph, $ G\unrhd_oC_n$ is an anti-magic graph.
PELABELAN ANTI AJAIB JARAK PADA GRAF HASIL KALI SISIR Soi Bau, Magdalena Clarita; Lapenangga Putra, Ganesha; Haning, Farly Oktriani; Aryanto
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.14.3.253-266.2025

Abstract

Diberikan graf tidak berarah $G= (V,E)$ dimana $V$ adalah himpunan simpul dan $E$ adalah himpunan sisi dari graf $G$. Graf $G$ merupakan graf dengan pelabelan anti ajaib jarak jika terdapat fungsi bijektif $f : V (G) \to \{1, 2, . . . , |V (G)|\}$ sehingga untuk setiap simpul u dan v, diperoleh $W(u)\neq W(v)$. Bobot titik $u \in V(G)$ didefinisikan sebagai $W(u)=\sum_{x\in N(u)} f(x)$ . Pada tulisan ini dibahas beberapa graf dengan operasi comb titik yang merupakan graf anti ajaib jarak. Hasilnya ialah pada beberapa kasus, graf $P_m \unrhd_o C_n,\; C_m \unrhd_o C_n,\; S_m \unrhd_o C_n,\; W_m \unrhd_o C_n,\; $ dan secara umum graf $G \unrhd_o C_n$ dan graf $G \unrhd_o W_n$ merupakan graf anti ajaib jarak.
ON THE ENERGY OF p-SEMISHADOW AND p-NEW DUPLICATE GRAPH: Investigating Adjacency Energy in Several Graph Operations shalsabilla, Az Zahra; ALGHOFARI, ABDUL ROUF; HIDAYAT, NOOR
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.14.3.196-207.2025

Abstract

Graph is mathematical structures used to represent relationships between objects as a vertex and edge (relationship between vertices). The energy of the graph is the absolute sum of the eigenvalues of its adjacency matrix, the graph representation matrix with entries 1 and 0. This article introduces a new graph operation, p-new duplicate, and determines energy of p-semishadow and p-new duplicate.
On ON LOCATING-DOMINATING SET OF THE CARTESIAN PRODUCT OF COMPLETE BIPARTITE GRAPHS AND A PATH OF ORDER TWO Saputro, Suhadi Wido; As-Shidiq, Ikhsan Rizqi Az-Zukruf
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.14.3.208-215.2025

Abstract

A set D is called as a locating-dominating set of a graph G if D is a dominating set of G such that every vertex outside D is uniquely identified by its neighbourhood within D. The locating-dominating number of G is the minimum cardinality of all locating-dominating sets of G. In this paper, we consider a Cartesian product graphs between a complete bipartite graphs Km1,m2 and a path of order two P2, denoted by Km1,m2P2. In particular, we determine the locating-dominating number of Km1,m2P2 for any values m1 and m2 at least 2.
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.}\\

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