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All Journal Pythagoras: Jurnal Matematika dan Pendidikan Matematika BIMASTER Epsilon: Jurnal Matematika Murni dan Terapan CAUCHY: Jurnal Matematika Murni dan Aplikasi Kubik Edumatsains Jurnal Matematika Sains dan Teknologi Zero : Jurnal Sains, Matematika, dan Terapan Teorema: Teori dan Riset Matematika Jambura Journal of Mathematics Mathvision : Jurnal Matematika Variabel Jurnal Pengabdian kepada Masyarakat Nusantara KUBIK: Jurnal Publikasi Ilmiah Matematika Jurnal Abdimas Bina Bangsa International Journal of Computing Science and Applied Mathematics-IJCSAM
Fransiskus Fran
Jurusan Matematika, Fakultas MIPA, Universitas Tanjungpura, Jl. Prof. Dr. Hadari Nawawi, Kota Pontianak 78124, Kalimantan Barat
Agriculture, Biological Sciences & Forestry Biochemistry, Genetics & Molecular Biology Chemistry Computer Science & IT Decision Sciences, Operations Research & Management Economics, Econometrics & Finance Education Languange, Linguistic, Communication & Media Mathematics Physics Social Sciences Transportation Other

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Bilangan Kromatik Permainan Graf Ubur-Ubur, Graf Siput, dan Graf Gurita M Luthfi Abdurahman; Helmi Helmi; Fransiskus Fran
Jambura Journal of Mathematics Vol 6, No 1: February 2024
Publisher : Department of Mathematics, Universitas Negeri Gorontalo

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.37905/jjom.v6i1.23958

Abstract

Graph coloring is the process of assigning colors to the vertices or edges of a graph. Specifically, coloring the vertices in graph coloring can be implemented in graph coloring games. This article aims to determine the game chromatic number of the jellyfish graph Jm,n, snail graph SIn, and octopus graph On. For example, give G as a simple, connected, and undirected graph and give two players, namely A as the first player and B as the secondary player. The two players A and B color all the vertices of graph G with available colors. The game's rules are that A must ensure that all vertices of graph G are colored, while B aims to prevent graph G from being uncolored. Players A and B take turns coloring the vertices of graph G, ensuring that the color of neighboring vertices must be different, with A taking the first turn. If all vertices have been colored, A wins the game, but A loses if some vertices remain uncolored despite available colors, A loses. The smallest value of k for which A has a winning strategy in the game with k colors is the game chromatic number, denoted as χg(G). This thesis discusses the graph coloring game of the tadpole graph Tm,n, broom graph Bn,d, jellyfish graph Jm,n, and tribune graph Tn to find the game chromatic number. The results show that player A uses a strategy to color the vertex with the highest degree in the graph, ensuring that player A always wins. Therefore, the game chromatic number of the jellyfish graph, snail graph, and octopus graph is χg (Jm,n) = 3 for m, n ≥ 1, and χg (SIn) = 3 for n ≥ 1, while χg (On) = 3 for n = 2, 3, 4; χg (On) = 4 for n ≥ 5.
Pelabelan Fibonacci Prima Ke-k Pada Graf H dan Graf Ulat H_n Nyemas Yupika Sari; Evi Noviani; Fransiskus Fran
KUBIK Vol 8 No 2 (2023): KUBIK: Jurnal Publikasi Ilmiah Matematika
Publisher : Department of Mathematics, Faculty of Science and Technology, UIN Sunan Gunung Djati Bandung

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.15575/kubik.v8i2.29290

Abstract

Artikel ini membahas tentang pelabelan Fibonacci prima ke-k pada sebuah graf sederhana G dengan himpunan simpul V(G) dan himpunan sisi E(G). Suatu graf G adalah graf Fibonacci prima ke-k jika terdapat pemetaan injektif f:V(G)→{F_k,F_(k+1),…,F_(k+n-1)} yang memetakan himpunan simpul V(G) ke himpunan bagian bilangan Fibonacci {F_k,F_(k+1),…,F_(k+n-1)}. F_k  merupakan bilangan Fibonacci yang berada pada urutan ke-k dimana k≤n dan k,n∈N. Untuk setiap sisi uv∈E(G) dengan u,v∈V(G)  berlaku f^* (uv)=gcd⁡(f(u),f(v))=1 dengan f^*:E(G)→N. Graf yang digunakan dalam penelitian ini adalah graf H dengan orde lebih besar atau sama dengan tiga dan graf ulat H_n  dengan orde lebih besar atau sama dengan dua. Penelitian ini bertujuan untuk mengkontruksi pelabelan Fibonacci prima ke-k pada graf H dan graf ulat H_n  serta membuktikan bahwa graf tersebut adalah graf Fibonacci prima ke-k.
Pelabelan Rata-Rata Geometris Graf Ular \mathbit{m}\mathbit{C}_\mathbit{n} Junjungan Dwipa Sakti Simanjuntak; Fransiskus Fran; Yudhi Yudhi
KUBIK Vol 11 No 1 (2026): KUBIK: Jurnal Publikasi Ilmiah Matematika
Publisher : Department of Mathematics, Faculty of Science and Technology, UIN Sunan Gunung Djati Bandung

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.15575/kubik.v11i1.38560

Abstract

Labeling on a graph is a mapping that assigns each element of the graph, namely a set of edges or a set of vertices to positive integer numbers, called labels. One type of graph labeling is geometric mean labeling, a variation of arithmetic mean labeling. The geometric mean labeling of a graph G = (V(G), E(G)) with vertices and edges is the injective function h from V(G) to {1,2,3, ..., q + 1} which induces a bijective function h* from E(G) to {1,2,3, ..., q} such that for each edge e = uv є E(G), h* (uv) = L√h(u)h(v)˩. A geometric mean graph is a graph that can be labeled with a geometric mean labeling. In this article, we discussed a geometric mean labeling on a snake graph mCn with n = 5,6,7,8 and m ≥ 1. The construction process of geometric mean labeling on the snake graph mCn with n = 5,6,7,8 and m ≥ 1 is done by labeling the vertices on the graph, which induces edge labels that meet the definition of geometric mean labeling. The results from the construction of geometric mean labeling patterns on the snake graph mCn with n = 5,6,7,8 and m ≥ 1 are geometric mean graphs.
Pelabelan Fibonacci Prima Ke-k Pada Graf H dan Graf Ulat H_n Nyemas Yupika Sari; Evi Noviani; Fransiskus Fran
KUBIK Vol 8 No 2 (2023): KUBIK: Jurnal Publikasi Ilmiah Matematika
Publisher : Department of Mathematics, Faculty of Science and Technology, UIN Sunan Gunung Djati Bandung

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.15575/kubik.v8i2.29290

Abstract

Artikel ini membahas tentang pelabelan Fibonacci prima ke-k pada sebuah graf sederhana G dengan himpunan simpul V(G) dan himpunan sisi E(G). Suatu graf G adalah graf Fibonacci prima ke-k jika terdapat pemetaan injektif f:V(G)→{F_k,F_(k+1),…,F_(k+n-1)} yang memetakan himpunan simpul V(G) ke himpunan bagian bilangan Fibonacci {F_k,F_(k+1),…,F_(k+n-1)}. F_k  merupakan bilangan Fibonacci yang berada pada urutan ke-k dimana k≤n dan k,n∈N. Untuk setiap sisi uv∈E(G) dengan u,v∈V(G)  berlaku f^* (uv)=gcd⁡(f(u),f(v))=1 dengan f^*:E(G)→N. Graf yang digunakan dalam penelitian ini adalah graf H dengan orde lebih besar atau sama dengan tiga dan graf ulat H_n  dengan orde lebih besar atau sama dengan dua. Penelitian ini bertujuan untuk mengkontruksi pelabelan Fibonacci prima ke-k pada graf H dan graf ulat H_n  serta membuktikan bahwa graf tersebut adalah graf Fibonacci prima ke-k.
Pelabelan Rata-Rata Geometris Graf Ular \mathbit{m}\mathbit{C}_\mathbit{n} Junjungan Dwipa Sakti Simanjuntak; Fransiskus Fran; Yudhi Yudhi
KUBIK Vol 11 No 1 (2026): KUBIK: Jurnal Publikasi Ilmiah Matematika
Publisher : Department of Mathematics, Faculty of Science and Technology, UIN Sunan Gunung Djati Bandung

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.15575/kubik.v11i1.38560

Abstract

Labeling on a graph is a mapping that assigns each element of the graph, namely a set of edges or a set of vertices to positive integer numbers, called labels. One type of graph labeling is geometric mean labeling, a variation of arithmetic mean labeling. The geometric mean labeling of a graph G = (V(G), E(G)) with vertices and edges is the injective function h from V(G) to {1,2,3, ..., q + 1} which induces a bijective function h* from E(G) to {1,2,3, ..., q} such that for each edge e = uv є E(G), h* (uv) = L√h(u)h(v)˩. A geometric mean graph is a graph that can be labeled with a geometric mean labeling. In this article, we discussed a geometric mean labeling on a snake graph mCn with n = 5,6,7,8 and m ≥ 1. The construction process of geometric mean labeling on the snake graph mCn with n = 5,6,7,8 and m ≥ 1 is done by labeling the vertices on the graph, which induces edge labels that meet the definition of geometric mean labeling. The results from the construction of geometric mean labeling patterns on the snake graph mCn with n = 5,6,7,8 and m ≥ 1 are geometric mean graphs.
Rainbow Antimagic Coloring of Closed Sunflower Graphs and Their Multilayer Extensions Fransiskus Fran; Muammar Rifqi; Evi Noviani; Raventino Raventino
CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 11, No 2 (2026): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI
Publisher : Mathematics Department, Maulana Malik Ibrahim State Islamic University of Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.18860/cauchy.v11i2.46193

Abstract

The challenge in rainbow antimagic coloring is not to eliminate repeated edge weights, but to arrange them without obstructing rainbow paths. We address this problem for closed sunflower graphs and their multilayer extensions, with edge colors determined by sums of distinct vertex labels. Explicit bijective labelings yield upper bounds, while vertex degrees, distances, and regular subgraphs provide complementary lower bounds. The resulting estimates hold throughout the defining parameter ranges of both families, and the smallest closed sunflower graph has rainbow antimagic connection number seven. For cycle lengths of at least ten that are congruent to two modulo four, a separate construction reduces the gap between the bounds to two colors. In the multilayer family, an alternating labeling scheme gives an upper bound that grows linearly with the number of layers for each fixed cycle length and recovers the general closed sunflower construction in the two-layer case. All constructions include a complete count of distinct edge weights and a verification of rainbow connectivity. The general labelings admit rainbow spanning trees, whereas the improved construction uses explicit paths and fewer colors than a rainbow spanning tree would require. This distinction demonstrates how coordinated color reuse can strengthen constructive bounds beyond the spanning-tree approach.
Co-Authors Alexander Andriko Andriko Annisatul Khairiah Asri Rahmawati Ayu Fitriani Bambang Poniman Bayu Prihandono Brella Glysentia Vilgalita Dany Riansyah Putra Dorotea Rahmawati Dwi Oktaviana Ervina Febyolga Esi Sari Evi Noviani Evi Utami Febby Desy Lia Felicia Yulita Kartika Sari Fransiska Evalia Helmi Helmi Ilhamsyah Junjungan Dwipa Sakti Simanjuntak Lidwina Evi Purwanti Lili Surai’ya M Luthfi Abdurahman Mariatul Kiftiah Meliana Pasaribu Muammar Rifqi Neno Juli Triami Nicko Nicko Nilamsari Kusumastuti Nora Yoshinta Sigalingging Novia Kristefany Kabang Novita Indah Saputri Nurhamzah Nurhamzah NUR’AINUL MIFTAHUL HUDA Nyemas Yupika Sari Onelia Rochmah Putri Romanda Raventino Raventino Resti Julia Susanti Rizky Oktaviani Robiandi Robiandi Robiandi Suryani Suryani Thedorus Junjun Tria Mutiara Umi Salmah Yuda Praja Yudhi Yundari, Yundari Yundari, Yundari