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All Journal BIMASTER Epsilon: Jurnal Matematika Murni dan Terapan Edumatsains Jurnal Matematika Sains dan Teknologi Teorema: Teori dan Riset Matematika Jambura Journal of Mathematics Mathvision : Jurnal Matematika Variabel Jurnal Abdimas Bina Bangsa
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 Decision Sciences, Operations Research & Management Education Languange, Linguistic, Communication & Media Mathematics Physics Social Sciences Transportation Other

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BILANGAN KROMATIK EQUITABLE PADA GRAF BINTANG, GRAF LOLIPOP, DAN GRAF PERSAHABATAN Yuda Praja; Fransiskus Fran; Nilamsari Kusumastuti
EPSILON: JURNAL MATEMATIKA MURNI DAN TERAPAN Vol 17, No 1 (2023)
Publisher : Mathematics Study Program, Faculty of Mathematics and Natural Sciences, Lambung Mangkurat

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.20527/epsilon.v17i1.8869

Abstract

Let G be a connected and undirected graph. Vertex coloring in a graph G is a mapping from the set of vertices in G to the set of colors such that every two adjacent vertices have different colors. There are many types of vertex coloring, such as complete coloring, k-differential coloring, and equitable coloring. Equitable coloring of G is a vertex coloring of G that satisfies the condition that for each induced color class it has an equitable cardinality with difference 0 or 1. The minimum number of colors used for such coloring of G is called the equitable chromatic number of G, denoted by χe(G). In this study, we only concern with graphs that have a central vertex, which means a vertex that is adjacent to every other vertex, in particular on the star graph (Sn), lollipop graph (Ln), and friendship graph (fn). This research aims to formulate the equitable chromatic number of the star graph (Sn), lollipop graph (Ln), and friendship graph (fn). The first step taken in this research is to apply vertex coloring to Sn, Ln, and fn. After that, the color classes of the vertex set are obtained and its cardinality is determined. Next, analyze that the applied vertex coloring meets the definition of equitable coloring. Then, prove that the number of colors used is minimum. Thus, the chromatic number for each graph is obtained and proved. Based on this research, the equitable chromatic number of Sn is ⌈n/2⌉ + 1, the equitable chromatic number of Ln is n, and the equitable chromatic number of fn is 3, for n = 1 and n + 1, for n ≥ 2.
PENDEKATAN PEMBELAJARAN BERBASIS PERMAINAN SEBAGAI UPAYA MENINGKATKAN KECERDASAN MATEMATIKA SISWA Mariatul Kiftiah; Nilamsari Kusumastuti; Bayu Prihandono; Yundari Yundari; Helmi Helmi; Evi Noviani; Fransiskus Fran; Yudhi Yudhi; Meliana Pasaribu; Nur’ainul Miftahul Huda
Jurnal Abdimas Bina Bangsa Vol. 5 No. 1 (2024): Jurnal Abdimas Bina Bangsa
Publisher : LPPM Universitas Bina Bangsa

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.46306/jabb.v5i1.979

Abstract

The perception of mathematics as a compulsory subject in school is often negative. To address this challenge, a service-learning initiative was implemented at SMAN 1 Sambas, employing a game-based pedagogy. Mathematics seminars and exhibitions were organized by Mathematics Study Program to enhance students' engagement and comprehension of mathematical concepts. The effectiveness of this approach was evaluated through a questionnaire, which revealed a high level of approval among students regarding the relevance, motivation, understanding of mathematical principles, problem-solving abilities, and playing skills in mathematics learning. This approach is expected to change students’ perception of mathematics and improve their learning outcomes
The Complexity of Octopus Graph, Friendship Graph, and Snail Graph Fransiskus Fran; Alexander; Yundari; Putri Romanda; Ervina Febyolga
EduMatSains : Jurnal Pendidikan, Matematika dan Sains Vol 9 No 1 (2024): July
Publisher : Fakultas Keguruan dan Ilmu Pendidikan, Universitas Kristen Indonesia

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.33541/edumatsains.v9i1.6042

Abstract

Graphs are basic structures that represent objects with nodes and relationships between objects with edges. Trees are one of the parts studied in graph theory along with finding the number of spanning trees of a graph such as octopus graph, friendship graph, and snail graph. The complexity of an octopus graph is strongly dependent on the number and length of tentacles, the complexity of a friendship graph is dependent on the number of triangle cycles, and the complexity of a snail graph is dependent on the number of edges and vertices located in the shell-like part of the snail. To calculate the number of spanning trees (τ(G)) of a graph, various calculations can be used, such as the extension of Kirchhoff's formula. The extension of Kirchhoff's formula uses the determinant of the adjacency matrix and degree matrix of the graph complement of a graph. Therefore, this research applies the extension of Kirchhoff's formula to obtain the complexity of octopus graph, friendship graph, and snail graph. From the analysis, it is obtained that for any n≥2, the number of spanning trees of octopus graph and friendship graph are τ(On )=1/5 √5 [((3+√5)/2)^n-((3-√5)/2)^n ] and τ(Fn )=3^n and the number of spanning trees of snail graph is τ(SIn )=2^(n+2)+3n∙2^(n-1) for n≥1.
MENENTUKAN INVERS DRAZIN DENGAN TEOREMA CAYLEY HAMILTON Nora Yoshinta Sigalingging; Fransiskus Fran; Nilamsari Kusumastuti
MathVisioN Vol 6 No 1 (2024): Maret 2024
Publisher : Prodi Matematika FMIPA Unirow Tuban

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.55719/mv.v6i1.998

Abstract

Setiap matriks tidak selalu memiliki invers. Matriks yang memiliki invers disebut matriks non-singular dan matriks yang tidak memiliki invers disebut matriks singular. Tetapi, matriks singular dapat ditentukan invers tergeneralisasinya. Invers tergeneralisasi adalah konsep aljabar linear yang digunakan dalam menentukan invers dari matriks singular. Salah satu invers tergeneralisasi yaitu invers Drazin dari suatu matriks singular  dilambangkan . Pada penelitian ini membahas cara menentukan invers Drazin yang merupakan salah satu invers tergeneralisasi dengan teorema Cayley Hamilton. Langkah-langkah untuk menentukan invers Drazin menggunakan teorema Cayley Hamilton, dimulai dengan mencari indeks suatu matriks singular . Indeks suatu matriks merupakan bilangan bulat non-negatif terkecil  yang memenuhi kondisi . Selanjutnya, dengan diperoleh indeks matriks dapat ditentukan matriks  dan  dengan menggunakan koefisien polinomial karakteristik dari matriks . Matriks  adalah matriks yang diperoleh dari  dan  adalah matriks yang diperoleh dari . Untuk menentukan invers Drazin dapat dihitung dengan .
Co-Authors Alexander Andriko Andriko Annisatul Khairiah 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 Lidwina Evi Purwanti Lili Surai’ya Mariatul Kiftiah Meliana Pasaribu Neno Juli Triami Nicko Nicko Nilamsari Kusumastuti Nora Yoshinta Sigalingging Novia Kristefany Kabang Novita Indah Saputri Nurhamzah Nurhamzah NUR’AINUL MIFTAHUL HUDA Putri Romanda Raventino Raventino Resti Julia Susanti Rizky Oktaviani Robiandi Robiandi Robiandi Umi Salmah Yuda Praja Yudhi Yundari, Yundari Yundari, Yundari