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Yulianti, Lyra
Department Of Mathematics And Data Science, Faculty Of Mathematics And Natural Sciences, Universitas Andalas, Indonesia
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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.
Dimensi Metrik Dari Graf Palem mellany, mellany; YULIANTI, LYRA; WELYYANTI, DES
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.
Bilangan Kromatik Lokasi Graf Helm Hm Dengan 3 ≤ m ≤ 9 Lessya, Kelson Novrianus; Welyyanti, Des; Yulianti, Lyra
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.
Co-Authors A. Asmiati Abdi Musra Abel, Latifa Azhar ADE NGESTU SULISTIO ADEK HAYATI PUTRI Admi Nazra Aisyah Nurinsani 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 Lessya, Kelson Novrianus M Fauzan Hardi Maharani Damayanti Mardhaningsih, Auli Mardhaningsih, Auli Mardimar, Kiki Khaira mellany mellany Mellany, Mellany Muhammad Rafif Fajri MUHAMMAD RANDA Muhardiansyah Muhardiansyah Mutiara Ramadhani Syafnur Nabila, Maya 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 Yanita Yanita YANITA YANITA, YANITA Zayendra, Siska - Zayendra, Siska - Zulakmal, Zulakmal ZULKARNAIN, DEBI