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All Journal Science and Technology Indonesia JMPM: Jurnal Matematika dan Pendidikan Matematika BAREKENG: Jurnal Ilmu Matematika dan Terapan Eksakta : Berkala Ilmiah Bidang MIPA Indonesian Journal of Combinatorics M A T H L I N E : Jurnal Matematika dan Pendidikan Matematika Jurnal Matematika UNAND Jurnal Saintika Unpam : Jurnal Sains dan Matematika Unpam InPrime: Indonesian Journal Of Pure And Applied Mathematics Warta Pengabdian Andalas: Jurnal Ilmiah Pengembangan Dan Penerapan Ipteks Jurnal Natural Limits: Journal of Mathematics and Its Applications
Des Welyyanti
Departemen Matematika Dan Sains Data, FMIPA, Universitas Andalas
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Bilangan Kromatik Lokasi Graf Helm Hm Dengan 3 ≤ m ≤ 9 Kelson Novrianus Lessya; Des Welyyanti; Lyra Yulianti
Jurnal Matematika UNAND Vol 12, No 3 (2023)
Publisher : Departemen Matematika dan Sains Data FMIPA Universitas Andalas Padang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.25077/jmua.12.3.222-228.2023

Abstract

Misalkan G = (V, E) adalah graf terhubung dan c suatu k−pewarnaan dari G. Kelas warna pada G adalah himpunan titik-titik yang berwarna i, dinotasikan dengan Si untuk 1 ≤ i ≤ k. Misalkan Π = {S1, S2. · · · , Sk} merupakan partisi terurut dari V (G) kedalam kelas-kelas warna yang saling bebas. Berdasarkan pewarnaan titik, maka representasi titik v terhadap Π disebut kode warna dari v, dinotasikan dengan cΠ(v) dari suatu titik v ∈ V (G) didefinisikan sebagai k−pasang terurut, yaitu: cΠ(v) = (d(v, S1), d(v, S2), · · · , d(v, Sk)) dengan d(v, Si) = min{d(v, x)|x ∈ Si} untuk 1 ≤ i ≤ k. Jika setiap titik pada G memiliki kode warna yang berbeda terhadap Π, maka c disebut pewarnaan lokasi. Banyaknya warna minimum yang digunakan disebut bilangan kromatik lokasi, dinotasikan dengan χL(G). Pada tulisan ini akan dibahas bilangan kromatik lokasi graf helm Hm dengan 3 ≤ m ≤ 9.
Dimensi Metrik Dari Graf Palem mellany mellany; LYRA YULIANTI; DES WELYYANTI
Jurnal Matematika UNAND Vol 12, No 4 (2023)
Publisher : Departemen Matematika dan Sains Data FMIPA Universitas Andalas Padang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.25077/jmua.12.4.276-282.2023

Abstract

Penelitian ini bertujuan mencari dimensi metrik dari garf palem CkPlSm, untuk k ≥ 3,l ≥ 2 dan m ≥ 2. Graf Palem CkPlSm merupakan graf yang dibangun oleh tiga graf, yaitu Graf Lingkaran Ck, Graf Lintasan Pl , dan Graf Bintang Sm. Penelitian ini diperoleh bahwa dimensi metrik graf palem adalah m, dim(H) = m.
The Bilangan Kromatik Lokasi Gabungan Graf Palem Nurinsani, Aisyah; Welyyanti, Des; Yulianti, Lyra
JMPM: Jurnal Matematika dan Pendidikan Matematika Vol 9 No 1 (2024): March - August 2024
Publisher : Prodi Pendidikan Matematika Universitas Pesantren Tinggi Darul Ulum Jombang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.26594/jmpm.v9i1.4828

Abstract

Vertex coloring of a graph is the coloring of vertices such that two adjacent vertices have different colors. The color code of a vertex is the distance from the vertex to the partition of the existing color set. A graph has a locating coloring if each vertex has a different color code. A palm graph is a graph constructed from a cycle graph, path graph, and star graph. A disjoint union of palm graphs is a disconnected graph with palm graphs as its components. The locating chromatic number of graph is the minimum colors of the graph to have locating coloring with k colors. In this paper, we determine the locating chromatic number of a disjoint union of palm graph.
On locating-chromatic number of helm graph H_m FOR 10m28 WELYYANTI, DES; SUTANTO, DASA; YULIANTI, LYRA
Jurnal Natural Volume 24 Number 3, October 2024
Publisher : Universitas Syiah Kuala

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.24815/jn.v24i3.33190

Abstract

Let G = (V,E) be a connected graph and c be a k-coloring of G. The color class S_i of G is a set of vertices given color i, for 1 i k. Let = {S_1,S_2,,S_k} be an ordered partition of V(G). The color code of a vertex v $in$ (element) V(G) is defined as the ordered k--tuplec_ (v)=(d(v,S_1),d(v,S_2),...,d(v,S_k)),where d(v,S_i) = min{d(v,x)| x $in$ (element) S_i} for 1 i k. If distinct vertices have distinct color codes, then c is called a locating-coloring of G. The locating-chromatic number _L (G) is the minimum number of colors in a locating-coloring of G. This paper discusses the locating-chromatic number of helm graph H_m for 10 m 28. Helm graph H_m is constructed by adding some leaves to the corresponding vertices of wheels W_m, for m 3.
LOCATING CHROMATIC NUMBER OF ONE-HEART GRAPH Hamdi, Muhammad; Welyyanti, Des; Sandy, Ikhlas Pratama
Jurnal Matematika UNAND Vol 14, No 1 (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.14.1.85-92.2025

Abstract

Bilangan kromatik lokasi merupakan konsep dari dimensi partisi graf dengan pewarnaan titik graf. Bilangan kromatik lokasi dari G, dinotasikan dengan χL(G) adalah jumlah warna minimum yang dipakai untuk pewarnaan lokasi. Dalam Artikel ini dijelaskan cara menentukan bilangan kromatik lokasi graf sehati. Metode yang dipakai agar diperolehnya bilangan kromatik lokasi graf sehati adalah dengan memperoleh nilai eksaknya. Hasil yang didapatkan dari bilangan kromatik lokasi graf sehati adalah χL(Hr_n)=4 untuk n=2 dan χL(Hr_n)=5 untuk n≥3.
LOCATING CHROMATIC NUMBER OF ONE-HEART GRAPH Hamdi, Muhammad; Welyyanti, Des; Sandy, Ikhlas Pratama
Jurnal Matematika UNAND Vol. 14 No. 1 (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.14.1.85-92.2025

Abstract

Bilangan kromatik lokasi merupakan konsep dari dimensi partisi graf dengan pewarnaan titik graf. Bilangan kromatik lokasi dari G, dinotasikan dengan χL(G) adalah jumlah warna minimum yang dipakai untuk pewarnaan lokasi. Dalam Artikel ini dijelaskan cara menentukan bilangan kromatik lokasi graf sehati. Metode yang dipakai agar diperolehnya bilangan kromatik lokasi graf sehati adalah dengan memperoleh nilai eksaknya. Hasil yang didapatkan dari bilangan kromatik lokasi graf sehati adalah χL(Hr_n)=4 untuk n=2 dan χL(Hr_n)=5 untuk n≥3.
The Metric Dimension and Partition Dimension of The Amalgamation of Complete Graphs Abdurrahman, Fatih; Welyyanti, Des; Sandy, Ikhlas Pratama
Mathline : Jurnal Matematika dan Pendidikan Matematika Vol. 10 No. 1 (2025): Mathline : Jurnal Matematika dan Pendidikan Matematika
Publisher : Universitas Wiralodra

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31943/mathline.v10i1.739

Abstract

In this paper, there is a section that identifies the aim of the research and makes it possible to suggest exploring the metric dimension and partition dimension of the amalgamation of complete graphs, which we would denote as Amal(Kn, v0)t. There are three steps conducted to achieve the research goals in this paper. To begin with, compute the lower bound of the metric dimension and the partition dimension of the graph Amal(Kn, v0)t. The second step is to find the upper bounds of the metric dimension and partition dimension of the graph Amal(Kn, v0)t by demonstrating that the representation of any vertex in Amal(Kn, v0)t is distinct. Finally, the exact values of the metric dimension and partition dimension of the graph Amal(Kn, v0)t are found if the lower and upper bounds are determined. The exact value of the metric dimension of the graph Amal(Kn, v0)t is denoted as dim(Amal(Kn, v0)t), while the exact value of the partition dimension is denoted as pd(Amal(Kn, v0)t). In this research, it is found that dim(Amal(Kn, v0)t) = (n - 2) for n, t ϵ N with n ≥ 3 and t ≥ 2. It is also found that pd(Amal(Kn, v0)t) = n for 2 ≤ t ≤ Cnn-1.
The Locating Chromatic Number of the Cyclic Chain Graph Abel, Latifa Azhar; Welyyanti, Des; Yulianti, Lyra; Permana, Dony
Science and Technology Indonesia Vol. 10 No. 3 (2025): July
Publisher : Research Center of Inorganic Materials and Coordination Complexes, FMIPA Universitas Sriwijaya

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.26554/sti.2025.10.3.958-962

Abstract

The locating chromatic number of graph G (χL(G)) combines the idea of the partition dimension and the chromatic number by considering the locations of the vertices of graph G. Let (Cni, m) be a cyclic chain graph, namely a group of blocks in the form of a cycle graph Cn1(1), Cn2(2), ···, Cni(i). The ni is the number of vertices on the i-th cycle, and m is the number of cycles, for ni ≥ 3, 1 ≤ i ≤ m, and m ≥ 2, and the vertex vi,⌈ni/2⌉+1 in Cni(i) is identified with the vertex vi,⌈ni/2⌉+1 in Cni+1(i+1). In this research, we determine χL(Cni, m) for ni ≥ 3, 1 ≤ i ≤ m, and m ≥ 2.
ON THE LOCATING CHROMATIC NUMBER OF DISJOINT UNION OF BUCKMINSTERFULLERENE GRAPHS Zulkarnain, Debi; Yulianti, Lyra; Welyyanti, Des; Mardimar, Kiki Khaira; Fajri, Muhammad Rafif
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 18 No 2 (2024): BAREKENG: Journal of Mathematics and Its Application
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol18iss2pp0915-0922

Abstract

Let be a connected non-trivial graph. Let c be a proper vertex-coloring using k colors, namely . Let be a partition of induced by , where is the color class that receives the color . The color code, denoted by , is defined as , where for , and is the distance between two vertices and in G. If all vertices in have different color codes, then is called as the locating-chromatic -coloring of . The locating-chromatic number of , denoted by , is the minimum such that has a locating coloring. Let be the Buckminsterfullerene graph on vertices. Buckminsterfullerene graph is a 3-connected planar graph and a member of the fullerene graphs, representing fullerene molecules in chemistry. In this paper, we determine the locating chromatic number of the disjoint union of Buckminsterfullerene graphs, denoted by .
THE LOCATING CHROMATIC NUMBER OF CHAIN(A,4,n) GRAPH Welyyanti, Des; Abel, Latifa Azhar; Yulianti, Lyra
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 19 No 1 (2025): BAREKENG: Journal of Mathematics and Its Application
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol19iss1pp353-360

Abstract

Let be a connected graph with a vertex coloringsuch that two adjacent vertices have different colors. We denote an ordered partition where is a color class with color-, consisting of vertices given color , for . The color code of a vertex in is a -vector: . where is the distance between a vertex in and for . If every two vertices and in have different color codes, , then is called the locating -coloring of . The minimum number of colors k needed in this coloring is defined as the locating chromatic number, denoted by . This paper determines the locating chromatic number of chain graph and the induction of two graphs . Graph is a cyclic graph , which is the identification of , for n>2.
Co-Authors Abdi Musra Abdurrahman, Fatih Abel, Latifa Azhar ADEK HAYATI PUTRI Admi Nazra Afrianti Afrianti Aisyah Nurinsani Alifaziz Arsyad Alifaziz Arsyad Angryanof, Uthary Putri Citra Mayora Daramenra, Romie Devianto, Dodi Efendi Efendi Effendi Effendi Eka Rahayu Nengsih A ELIZIA AUGUSTIN Elva Rahimah Fadhila Radiah Anas Fajri, Muhammad Rafif Fajri, Muhammad Rafif Fakhri Zikra Febria Angraini Fitri - Anggalia Hamdi, Muhammad Haripamyu Haripamyu Hazmira Yozza Ikhlas Pratama Sandy Kelson Novrianus Lessya KIKI KHAIRA MARDIMAR Laila Hidayati Laila Hidayati Lessya, Kelson Novrianus Lyra Yulianti Lyra Yulianti Mardimar, Kiki Khaira Mega Silvia Meiza Fiqrul Hanif MELATI NUR mellany mellany Mellany, Mellany Muhammad Rafif Fajri MUHAMMAD RANDA Mulyani Putri, Susi Muthia Muhana Mutiara Ramadhani Syafnur Nada Andriani Nada Andriani Narwen Narwen Noverina Alfiany Nurinsani, Aisyah Nurwijayanti Permana, Dony Pratama Sandy, Ikhlas REFI ALKADAR Rendy Aditya Pratama Romie Daramenra RUVIQA PUTRI SOLEHA Sagita Putri, Vella Saputro, Suhadi Wido Suci Rahma Putri Sugesti Sugesti SUTANTO, DASA Sutra Lidya Pritama Syafruddin . Tika Apriliza Uthary Putri Angryanof Wahyuni, Annisa Yanita Yanita Yanita, Yanita Yanuar, Ferra Yulianti, Lyra Yulianti, Lyra Zahara Zahara ZULKARNAIN, DEBI