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CGANT JOURNAL OF MATHEMATICS AND APPLICATIONS
Published by Universitas Jember
ISSN : -     EISSN : 27227774     DOI : https://doi.org/10.25037/cgantjma
Core Subject : Science, Education,
Computer Science & IT Other
Subjects suitable for publication include, the following fields of: Degree Diameter Problem in Graph Theory Large Graphs in Computer Science Mathematical Computation of Graph Theory Graph Coloring in Atomic and Molecular Graph Labeling in Coding Theory and Cryptography Dimensions of graphs on Control System Rainbow Connection in Delivery Design System Ramsey Theory and Its Application on Physics Graph Theory in Communication and Electrical Networks Graph Theory in Quantum Mechanics and Thermodynamics Spectral Graph Theory in Vibration and Noise Graph Theory in Statistical Physics and Mechanics Graph theory in Network of Quantum Oscillators Applied Mathematics on Environment, Biophysics and Engineering Machine Learning and Artificial Neural Networks Mathematical and Computational Education
Arjuna Subject : Matematika - Matematika Diskrit dan Kombinatori
Articles 8 Documents
 1 
Search results for , issue "Vol 3, No 1 (2022): CGANT JOURNAL OF MATHEMATICS AND APPLICATIONS" : 8 Documents clear
Rainbow Vertex Connection Number pada Keluarga Graf Roda Firman Firman; Dafik Dafik; Ermita Rizki Albirri
CGANT JOURNAL OF MATHEMATICS AND APPLICATIONS Vol 3, No 1 (2022): CGANT JOURNAL OF MATHEMATICS AND APPLICATIONS
Publisher : jcgant

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (498.996 KB) | DOI: 10.25037/cgantjma.v3i1.71

Abstract

The rainbow vertex connection was first introduced by krivelevich and yuster in 2009 which is an extension of the rainbow connection. Let graph $G =(V,E)$ is a connected graph. Rainbow vertex-connection is the assignment of color to the vertices of a graph $G$, if every vertex on graph $G$ is connected by a path that has interior vertices with different colors. The minimum number of colors from the rainbow vertex coloring in graph $G$ is called rainbow vertex connection number which is denoted $rvc(G)$. The result of the research are the rainbow vertex connection number of family wheel graphs.
Pewarnaan Titik Ketakteraturan Lokal Refleksif pada Keluarga Graf Tangga Rizki Aulia Akbar; Dafik Dafik; Rafiantika Megahnia Prihandini
CGANT JOURNAL OF MATHEMATICS AND APPLICATIONS Vol 3, No 1 (2022): CGANT JOURNAL OF MATHEMATICS AND APPLICATIONS
Publisher : jcgant

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (690.435 KB) | DOI: 10.25037/cgantjma.v3i1.72

Abstract

Let a simple and connected graph $G=(V,E)$ with the vertex set $V(G)$ and the edge set E(G). If there is a mapping $f$: $V(G)$ $\rightarrow$ ${0,2,…,2k_v}$ and $f$: $E(G)$ $\rightarrow$ ${1,2,…,k_e}$ as a function of vertex and edge irregularities labeling with $k=max$ ${2k_v,k_e}$ for $k_v$ and $k_e$ natural numbers and the associated weight of vertex $u,v \in V(G)$ under $f$ is $w(u)=f(u)+\sum_{u,v\in E(G)}f(uv)$. Then the function $f$ is called a local vertex irregular reflexive labeling if every adjacent vertices has distinct vertex weight. When each vertex of graph $G$ is colored with a vertex weight $w(u,v)$, then  graph $G$ is said to have a local vertex irregular reflexive coloring. Minimum number of vertex weight is needed to color the vertices in graf $G$ such that any adjacent vertices are not have the same color is called a local vertex irregular reflexive chromatic number, denoted by $\chi_{(lrvs)}(G)$. The minimum $k$ required such that $\chi_{(lrvs)}(G)=\chi(G)$ where $\chi(G)$ is chromatic number of proper coloring on G is called local reflexive vertex color strength, denoted by $lrvcs(G)$. In this paper, we will examine the local reflexive vertex color strength of local vertex irregular reflexive coloring on the family of ladder graph.
Pewarnaan Titik Ketakteraturan Lokal Refleksif pada Keluarga Graf Roda Tommi Sanjaya Putra; Dafik Dafik; Ermita R Albirri
CGANT JOURNAL OF MATHEMATICS AND APPLICATIONS Vol 3, No 1 (2022): CGANT JOURNAL OF MATHEMATICS AND APPLICATIONS
Publisher : jcgant

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (645.265 KB) | DOI: 10.25037/cgantjma.v3i1.73

Abstract

All graph in this paper is simple and connected graph where $V(G)$ is vertex set and $E(G)$ is edge set. Let function $f : V(G)\longrightarrow \{0, 2,..., 2k_v\}$ as vertex labeling and a function $f: E(G)\longrightarrow \{1, 2,..., k_e\}$ as edge labeling where $k=max\{2k_v,k_e\}$ for $k_v,k_e$ are natural number. The weight of vertex $ u,v\in V(G) $ under $f$ is $w(u)=f(u)+ \Sigma_{uv \in E(G)} f(uv)$. In other words, the function $f$ is called local vertex irregular reflexive labeling if every two adjacent vertices has distinct weight and weight of a vertex is defined as the sum of the labels of vertex and the labels of all edges incident this vertex When we assign each vertex of $G$ with a color of the vertex weight $w(uv)$, thus we say the graph G admits a local vertex irregular reflexive coloring. The minimum number of colors produced from local vertex irregular reflexive coloring of graph $G$ is reflexive local irregular chromatic number denoted by $\chi_{lrvs}(G).$ Furthermore, the minimum $k$ required such that $\chi_{lrvs}(G)=\chi(G)$ is called a local reflexive vertex color strength, denoted by \emph{lrvcs}$(G)$. In this paper, we learn about the local vertex irregular reflexive coloring and obtain \emph{lrvcs}$(G)$ of wheel related graphs.
Pewarnaan Titik pada Keluarga Graf Sentripetal Istamala Idha Retnoningsih; Dafik Dafik; Saddam Hussen
CGANT JOURNAL OF MATHEMATICS AND APPLICATIONS Vol 3, No 1 (2022): CGANT JOURNAL OF MATHEMATICS AND APPLICATIONS
Publisher : jcgant

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (1025.76 KB) | DOI: 10.25037/cgantjma.v3i1.75

Abstract

The graph $G$ is defined as a pair of sets $(V,E)$ denoted by $G=(V,E)$, where $V$ is a non-empty vertex set and $E$ is an edge set may be empty connecting a pair of vertex. Two vertices $u$ and $v$ in the graph $G$ are said to be adjacent if $u$ and $v$ are endpoints of edge $e=uv$. The degree of a vertex $v$ on the graph $G$ is the number of vertices adjacent to the vertex $v$. In this study, the topic of graphs is vertex coloring will be studied. Coloring of a graph is giving color to the elements in the graph such that each adjacent element must have a different color. Vertex coloring in graph $G$ is assigning color to each vertex on graph $G$ such that the adjecent vertices $u$ and $v$ have different colors. The minimum number of colorings produced to color a vertex in a graph $G$ is called the vertex chromatic number in a graph $G$ denoted by $\chi(G)$.
Pengembangan Perangkat Pembelajaran RBL-STEM Untuk Meningkatkan Metaliterasi Siswa Menerapkan Konsep Relasi Fungsi Dalam Menyelesaikan Masalah Dekorasi Teselasi Wallpaper Sufirman Sufirman; Dafik Dafik; Arif Fatahillah
CGANT JOURNAL OF MATHEMATICS AND APPLICATIONS Vol 3, No 1 (2022): CGANT JOURNAL OF MATHEMATICS AND APPLICATIONS
Publisher : jcgant

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (1048.364 KB) | DOI: 10.25037/cgantjma.v3i1.69

Abstract

Dalam menyelesaikan persoalan matematika, terlebih yang mengintegrasikan permasalahan di kehidupan sehari hari diperlukan kemampuan metaliterasi siswa. Metaliterasi merupakan kerangka berpikir yang menyeluruh dan menjadi sumber referensi mandiri yang bersifat luas dibandingkan dengan jenis literasi lainnnya. Kemampuan metaliterasi siswa saat ini dapat dibilang rendah karena masih tergolong baru dan pembelajaran belum sepenuhnya menggunakan Internet of Things dalam pelaksanaannya. Oleh karena itu, dalam penelitian ini menggunakan model pembelajaran Research Based Learning dengan pendekatan STEM yang berfokus pada pemecahan masalah dekorasi teselasi wallpaper. Pada permasalahan ini, siswa merepresentasikan model dekorasi wallpaper kedalam bentuk titik dan garis untuk menemukan kombinasi warna yang sesuai. Selanjutnya dengan menggunakan konsep relasi fungsi, siswa dapat menemukan pola pewarnaan dari dekorasi tersebut. Dalam kegiatan pembelajaran, permasalahan STEM yang diangkat akan dikembangkan framework integrasi RBL-STEM untuk meningkatkan metaliterasi siswa. Hasil penelitian yang diperoleh berupa sintaks baru yang efektif dalam memecahkan permasalahan teselasi wallpaper dengan model RBL-STEM yang melibatkan relasi fungsi, perangkat pembelajaran RBL-STEM dan potret fase kemampuan metaliterasi siswa
Pewarnaan Pelangi Antiajaib pada Amalgamasi Graf Riniatul Nur Wahidah; Dafik Dafik; Ermita Rizki Albirri
CGANT JOURNAL OF MATHEMATICS AND APPLICATIONS Vol 3, No 1 (2022): CGANT JOURNAL OF MATHEMATICS AND APPLICATIONS
Publisher : jcgant

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (496.647 KB) | DOI: 10.25037/cgantjma.v3i1.76

Abstract

Let $G$ is a connected graph with vertex set $V(G)$ and edge set $E(G)$. The side weights for $uv\in E(G) $ bijective function $f:V(G)\rightarrow\{1,2,\dots, |V(G)|\}$ and $ w(uv)= f(u)+f(v) $ . If each edge has a different weight, the function $f$ is called an antimagic edge point labeling.  Is said to be a rainbow path, if a path $P$ on the graph labeled vertex $G$ with every two edges $ ,u'v'\in E(P) $ fulfill  $ w(uv)\neq w(u'v') $. If for every two vertices $u,v \in V(G)$, their path $uv$ rainbow, $f$ is called the rainbow antimagic labeling of the graph $G$. Graph G is an antimagic coloring of the rainbow if we for each edge $uv$ weight color side  $w(uv)$. The smallest number of colors induced from all sides is the rainbow antimagic connection number $G$, denoted by $rac(G)$. This study shows the results of the rainbow antimagic connection number from amalgamation graph.
Analisis rainbow vertex connection pada beberapa graf khusus dan operasinya Ida Ariska; Ika Hesti Agustin; Kusbudiono Kusbudiono
CGANT JOURNAL OF MATHEMATICS AND APPLICATIONS Vol 3, No 1 (2022): CGANT JOURNAL OF MATHEMATICS AND APPLICATIONS
Publisher : jcgant

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.25037/cgantjma.v3i1.78

Abstract

The vertex colored graph G is said rainbow vertex cennected, if for every two vertices are connected by a path whose internal vertices have distinct colors. The rainbow vertex connection number of G, denoted by rvc(G), is the smallest number of colors that are needed in order to make G rainbow vertex connected. On this research, will be raised the issue of how to produce graphs the results of some special graph and how to find the rainbow vertex connection. Operation that use cartesian product, crown product, and shackle. Theorem in this research rainbow vertex connection number in graph the results of operations Wd3,m □ Pn,,Wd3,m ⵙ Pn, and shack(Btm,v,n).
Penerapan Teknik Partisi Langkah Kuda Papan Catur pada Pelabelan Super (a,d)-P_2 (▷) ̇ H-Antimagic Total Covering Sebarang Dua Graf dan Aplikasinya A H Rahmatillah; I H Agustin; Dafik Dafik
CGANT JOURNAL OF MATHEMATICS AND APPLICATIONS Vol 3, No 1 (2022): CGANT JOURNAL OF MATHEMATICS AND APPLICATIONS
Publisher : jcgant

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.25037/cgantjma.v3i1.79

Abstract

Let  be a finite collection of simple, nontrivial and undirected graphs. A graph  is as antimagic total covering if there is bijectif  function  for every subgraph in which isomorfic to  and the total  weight,  form arithmetic sequence , in which a,b are integers and n is a number of graph cover of which the result of total comb product operation. A antimagic total covering  is as "super" if smallest label is used for vertex labelling. The way for labelling a graph this time, using a knight move partition techniques application. The graph use total comb product operation . Take a copy of  and a number  of , then put the  copy of -sequence in graph vertex  to -sequence vertex of  and put the  copy of -sequence in graft edge  to -sequence edge of  is definition of total comb product. In this article, will be investigated about Knight Move Partition Techniques Application in Labelling Super Antimagic Total Covering for Any Two Graphs and Its Application (in Constructing Ciphertext).

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