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All Journal Science and Technology Indonesia JMPM: Jurnal Matematika dan Pendidikan Matematika BAREKENG: Jurnal Ilmu Matematika dan Terapan Limits: Journal of Mathematics and Its Applications Jambura Journal of Mathematics Jurnal Hilirisasi IPTEKS (JHI) Eksakta : Berkala Ilmiah Bidang MIPA Indonesian Journal of Combinatorics Jurnal Matematika UNAND Jurnal Lebesgue : Jurnal Ilmiah Pendidikan Matematika, Matematika dan Statistika Jurnal Natural Limits: Journal of Mathematics and Its Applications
Yulianti, Lyra
Department Of Mathematics And Data Science, Faculty Of Mathematics And Natural Sciences, Universitas Andalas, Indonesia
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Dimensi Partisi Graf Thorn dari Graf Kincir ?Wd?_2^m untuk m=1,2,3 Zayendra, Siska -; Mardhaningsih, Auli; Yulianti, Lyra; Effendi, Effendi
JMPM: Jurnal Matematika dan Pendidikan Matematika Vol 4 No 1: March - August 2019
Publisher : Prodi Pendidikan Matematika Universitas Pesantren Tinggi Darul Ulum Jombang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.26594/jmpm.v4i1.1434

Abstract

Misalkan G = (V, E)  adalah  suatu  graf terhubung.  Himpunan  titik  V(G) dipartisi  menjadi  beberapa  partisi,  dan  ? = {S1, S2, ..., Sk } sebagai  himpunan yang berisikan  k-partisi  tersebut.  Misalkan  v ? V (G),  representasi  v terhadap ? didefinisikan sebagai r(v|?)  = (d(v, S1), .., d(v, Sk )).  ? disebut  partisi  penye- lesaian jika setiap  titik  di G mempunyai  representasi  yang berbeda  terhadap ?. Kardinalitas yang minimum dari partisi  penyelesaian disebut  dimensi partisi  dari G, ditulis pd(G). Thorn  dari graf G, dengan parameter l1, l2, . . . , ln diperoleh dengan menambahkan daun sebanyak li ke titik vi  dari graf G, untuk  i ? {1, . . . , n}, dengan  li  ? 1.  Graf  thorn  dari  graf G dinotasikan  dengan  T h(G, l1, l2 , . . . , ln ). Pada  jurnal ini ditentukan dimensi partisi  graf thorn  dari graf kincir W d2m   untuk m = 1, 2, 3, dinotasikan  dengan T h(W d2m , l0 , l1, . . . , l2m ), untuk  i = 0, 1, 2, .., 2m.Kata kunci: Dimensi partisi,  graf thorn, graf kincir
MATRIKS TRANSFORMASI OPERATOR VECD* MENJADI VECH^ Alsbaldo, Yuco; Yanita, Yanita; Yulianti, Lyra
Jurnal Lebesgue : Jurnal Ilmiah Pendidikan Matematika, Matematika dan Statistika Vol. 6 No. 1 (2025): Jurnal Lebesgue : Jurnal Ilmiah Pendidikan Matematika, Matematika dan Statistik
Publisher : LPPM Universitas Bina Bangsa

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.46306/lb.v6i1.940

Abstract

This article discusses a new matrix operator that is constructed differently from the vech operator and the vecd operator by stacking the main diagonal entries (supra-diagonal) and entries of a square matrix. This operator, called  operator, explicitly constructs a matrix that transforms  into , where  is an  square matrix, and then obtains the properties of the transformation matrix
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 COMMUTATION MATRIX Yanita, Yanita; Yulianti, Lyra
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 17 No 4 (2023): BAREKENG: Journal of Mathematics and Its Applications
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol17iss4pp1997-2010

Abstract

The commutation matrix is a matrix that transforms any vec matrix , to vec transpose . In this article, three definitions of the commutation matrix are presented in different ways. It is shown that these three definitions are equivalent. Proof of the equivalent uses the properties in the Kronecker product on the matrix. We also gave the example of the commutation matrix using three ways as Moreover, in this study, we investigate the properties of the commutation matrix related to its transpose and the relation between the vec matrix and the vec transpose matrix using the commutation matrix. We have that the transpose and the inverse of the commutation matrix is its transpose.
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.
Bilangan Kromatik Lokasi Pada Graf Amalgamasi Kipas Berekor Des Welyyanti; Nada Andriani; Lyra Yulianti
Limits: Journal of Mathematics and Its Applications Vol. 20 No. 1 (2023): Limits: Journal of Mathematics and Its Applications Volume 20 Nomor 1 Edisi Ma
Publisher : Pusat Publikasi Ilmiah LPPM Institut Teknologi Sepuluh Nopember

Show Abstract | Download Original | Original Source | Check in Google Scholar

Abstract

Misalkan G adalah graf terhubung dengan himpunan simpul V dan himpunan sisi E, serta c adalah suatu k-pewarnaan dari G. Misalkan P adalah partisi terurut dari V(G) ke dalam kelas warna yang dihasilkan, yaitu P = {S1, S2, ..., Sk}. Berdasarkan pewarnaan simpul, maka representasi simpul v terhadap partisi P disebut kode warna dari v, dan dinotasikan dengan c_P(v). Kode warna c_P(v) dari suatu simpul v yang termasuk dalam V(G) didefinisikan sebagai pasangan terurut sebanyak k buah.
Dimensi Metrik Graf Buckminsterfullerene-Subdivisi dan Buckminsterfullerene-Star Lyra Yulianti; Laila Hidayati; Des Welyyanti
Limits: Journal of Mathematics and Its Applications Vol. 20 No. 2 (2023): Limits: Journal of Mathematics and Its Applications Volume 20 Nomor 2 Edisi Ju
Publisher : Pusat Publikasi Ilmiah LPPM Institut Teknologi Sepuluh Nopember

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Abstract

Misalkan terdapat graf Buckminsterfullerene dengan 60 titik. Graf Buckminsterfullerene-subdivisi , dinotasikan , , dikonstruksi dengan cara melakukan operasi subdivisi terhadap satu sisi tertentu di , yaitu penyisipan sebanyak titik di sisi tersebut. Selanjutnya, Graf Buckminsterfullerene-star , dinotasikan , dikonstruksi dengan cara mengidentifikasi masing-masing satu titik daun dari lima graf bintang dengan titik yang bersesuaian di Pada artikel ini akan ditentukan dimensi metrik dari dan untuk .
Dimensi Metrik Amalgamasi Graf Theta Des Welyyanti; Alifaziz Arsyad; Lyra Yulianti
Limits: Journal of Mathematics and Its Applications Vol. 20 No. 2 (2023): Limits: Journal of Mathematics and Its Applications Volume 20 Nomor 2 Edisi Ju
Publisher : Pusat Publikasi Ilmiah LPPM Institut Teknologi Sepuluh Nopember

Show Abstract | Download Original | Original Source | Check in Google Scholar

Abstract

Misalkan G = (V, E) adalah suatu graf terhubung dengan himpunan titik V(G) dan himpunan sisi E(G). Misalkan u dan v adalah titik-titik dalam graf terhubung G, panjang lintasan terpendek dari u ke v pada G dinotasikan d(u, v). Jika S adalah suatu himpunan terurut dari titik-titik dalam graf terhubung G dan titik V E V(G), maka representasi dari titik v terhadap S, dinotasikan r(v | S), adalah vektor d(v, s1), d(v, s2), ..., d(v, sk) untuk setiap si E S. Jika r(v | S) untuk setiap titik V E V(G) berbeda, maka S dinamakan himpunan pembeda dari G. Himpunan pembeda dengan kardinalitas minimum dinamakan himpunan pembeda minimum, dan kardinalitas dari himpunan pembeda minimum dinamakan dimensi metrik (metric dimension) dari G, dinotasikan dim(G). Pada penelitian ini dibahas tentang dimensi metrik amalgamasi graf Theta.
Bilangan Kromatik Lokasi Amalgamasi Graf Theta Des Welyyanti; Uthary Putri Angryanof; Lyra Yulianti
Limits: Journal of Mathematics and Its Applications Vol. 21 No. 3 (2024): Limits: Journal of Mathematics and Its Applications Volume 21 Nomor 3 Edisi No
Publisher : Pusat Publikasi Ilmiah LPPM Institut Teknologi Sepuluh Nopember

Show Abstract | Download Original | Original Source | Check in Google Scholar

Abstract

Misalkan adalah suatu pewarnaan titik pada graf dimana , untuk dan yang bertetangga di . Kode warna dari adalah pasang terurut dimana untuk . Jika setiap titik memiliki kode warna yang berbeda, maka disebut pewarnaan lokasi dari . Banyaknya warna minimum yang digunakan untuk pewarnaan lokasi termasuk bilangan kromatik lokasi dari dan dinotasikan dengan Pada artikel ini akan dibahas mengenai bilangan kromatik lokasi amalgamasi graf theta.
Co-Authors A. Asmiati Abdi Musra Abel, Latifa Azhar ADE NGESTU SULISTIO ADEK HAYATI PUTRI Admi Nazra Aisyah Nurinsani Alifaziz Arsyad Alifaziz Arsyad Alsbaldo, Yuco Angdini Putri F Angryanof, Uthary Putri Auli Mardhaningsih C. Ike Tri Widyastuti Daramenra, Romie DEBI ZULKARNAIN Des Welyyanti Effendi Effendi Effendi Effendi Eka Purwanti Elva Rahimah Fadillah Fadillah Fajri, Muhammad Rafif Fakhri Zikra Fawwaz Fakhrurrozi Hadiputra Fifi Febrianti Fitri - Anggalia Haves Derindo Hazmira Yozza Hidayati Rais Izzati Rahmi HG Kelson Novrianus Lessya Khairannisa Al Azizu KIKI KHAIRA MARDIMAR Laila Hidayati Laila Hidayati Lessya, Kelson Novrianus M Fauzan Hardi Maharani Damayanti Mardhaningsih, Auli Mardhaningsih, Auli Mardimar, Kiki Khaira Maya Nabila mellany mellany Mellany, Mellany Muhammad Rafif Fajri MUHAMMAD RANDA Muhardiansyah Muhardiansyah Mutiara Ramadhani Syafnur Nada Andriani Nada Andriani Nadia Nadia Nadia Nadia Nailul Yuni Permataputri Narwen Narwen NINDI MAULA AZIZAH Nurhasanah Nurhasanah Nurinsani, Aisyah Permana, Dony Putri Wulan Sari Risya Hazani Utari RIZKI REFORMAN Robi Nugraha Sayi Shelli Fitrianda Siska - Zayendra Sri Hariyani Suci Yefri Fadillah Suciana Budi Aryani SUTANTO, DASA Syafrizal Sy Syafrizal Sy Syafrizal Sy . Syafwan, Mahdhivan Tika Apriliza ULFA RAHAYU SY Uthary Putri Angryanof Yanita Yanita YANITA YANITA, YANITA Zayendra, Siska - Zayendra, Siska - Zulakmal, Zulakmal ZULKARNAIN, DEBI