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CGANT JOURNAL OF MATHEMATICS AND APPLICATIONS

cgant
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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

Search results for , issue "Vol 2, No 1 (2021): CGANT JOURNAL OF MATHEMATICS AND APPLICATIONS" : 8 Documents clear

Analisa Pewarnaan Total r-Dinamis pada Graf Lintasan dan Graf Hasil Operasi Desi Febriani Putri; Dafik Dafik; Kusbudiono Kusbudiono
CGANT JOURNAL OF MATHEMATICS AND APPLICATIONS Vol 2, No 1 (2021): CGANT JOURNAL OF MATHEMATICS AND APPLICATIONS
Publisher : jcgant

Graph coloring began to be developed into coloring dynamic. One of the developments of dynamic coloring is $r$-dynamic total coloring. Suppose $G=(V(G),E(G))$ is a non-trivial connected graph. Total coloring is defined as $c:(V(G) \cup E(G))\rightarrow {1,2,...,k}, k \in N$, with condition two adjacent vertices and the edge that is adjacent to the vertex must have a different color. $r$-dynamic total coloring defined as the mapping of the function $c$ from the set of vertices and edges $(V(G)\cup E(G))$ such that for every vertex $v \in V(G)$ satisfy $|c(N(v))| = min{[r,d(v)+|N(v)|]}$, and for each edge $e=uv \in E(G)$ satisfy $|c(N(e))| = min{[r,d(u)+d(v)]}$. The minimal $k$ of color is called $r$-dynamic total chromatic number denoted by $\chi^{\prime\prime}(G)$. The $1$-dynamic total chromatic number is denoted by $\chi^{\prime\prime}(G)$, chromatic number $2$-dynamic denoted with $\chi^{\prime\prime}_d(G)$ and $r$-dynamic chromatic number denoted by $\chi^{\prime\prime}_r(G)$. The graph that used in this research are path graph, $shackle$ of book graph $(shack(B_2,v,n)$ and \emph{generalized shackle} of graph \emph{friendship} $gshack({\bf F}_4,e,n)$.

Pewarnaan Sisi r-Dinamis pada Graf Khusus dan Graf Operasi Sakel Viqedina Rizky Noviyanti; Kusbudiono Kusbudiono; Ika Hesti Agustin; Dafik Dafik
CGANT JOURNAL OF MATHEMATICS AND APPLICATIONS Vol 2, No 1 (2021): CGANT JOURNAL OF MATHEMATICS AND APPLICATIONS
Publisher : jcgant

Let $G=(V(G),E(G))$ be a nontrivial connected graph. The edge coloring is defined as $c:E(G) \rightarrow \{1,2,...,k\}, k \in N$, with the condition that no adjacent edges have the same color. \emph{k}-color \emph{r}-dynamic is an edge coloring of \emph{k}-colors such that each edge in neighboring $E(G)$ is at least min $\{r,d( u)+d(v)-2\}$ has a different color. The dynamic \emph{r}-edge coloring is defined as a mapping of $c$ from $E(G)$ such that $|c(N(uv))|$ = min$\{r,d(u)+d(v)- 2\}$, where $N(uv)$ is the neighbor of $uv$ and $c(N(uv))$ is the color used by the neighboring side of $uv$. The minimum value of $k$ so that the graph $G$ satisfies the \emph{k}-coloring \emph{r}-dynamic edges is called the dynamic \emph{r}-edge chromatic number. 1-dynamic chromatic number is denoted by $\lambda(G)$, 2-dynamic chromatic number is denoted by $\lambda_d(G)$ and for dynamic \emph{r}-chromatic number is denoted by $\lambda_r(G)$. The graphs that used in this study are graph $TL_n$, $TCL_n$ and the switch operation graph $shack(H_{2,2},v,n)$.

Analisa Antimagic Total Covering Super pada Eksponensial Graf Khusus dan Aplikasinya dalam Mengembangkan Chipertext Hani'ah Zakin; Ika Hesti Agustin; Kusbudiono Kusbudiono; Dafik Dafik
CGANT JOURNAL OF MATHEMATICS AND APPLICATIONS Vol 2, No 1 (2021): CGANT JOURNAL OF MATHEMATICS AND APPLICATIONS
Publisher : jcgant

Let ${H_i}$ be a finite collection of simple, nontrivial and undirected graphs and let each $H_i$ have a fixed vertex $v_j$ called a terminal. The amalgamation $H_i$ as $v_j$ as a terminal is formed by taking all the $H_i$'s and identifying their terminal. When $H_i$ are all isomorphic graphs, for any positif integer $n$, we denote such amalgamation by $G={\rm Amal}(H,v,n)$, where $n$ denotes the number of copies of $H$. The graph $G$ is said to be an $(a, d)$-$H$-antimagic total graph if there exist a bijective function $f: V(G) \cup E(G) \rightarrow \{1, 2,\dots ,|V (G)| + |E(G)|\}$ such that for all subgraphs isomorphic to $H$, the total $H$-weights $w(H)= \sum_{v\in V(H)}f(v)+\sum_{e\in E(H)}f(e)$ form an arithmetic sequence $\{a, a + d, a +2d,...,a+(t - 1)d\}$, where $a$ and $d$ are positive integers and $t$ is the number of all subgraphs isomorphic to $H$. An $(a,d)$-$H$-antimagic total labeling $f$ is called super if the smallest labels appear in the vertices. In this paper, we study a super $(a, d)$-$H$ antimagic total labeling of $G={\rm Amal}(H,v,n)$ and its disjoint union when $H$ is a complete graph.

Metric Dimension dan Non-Isolated Resolving Number pada Beberapa Graf Wahyu Nikmatus Sholihah; Dafik Dafik; Kusbudiono Kusbudiono
CGANT JOURNAL OF MATHEMATICS AND APPLICATIONS Vol 2, No 1 (2021): CGANT JOURNAL OF MATHEMATICS AND APPLICATIONS
Publisher : jcgant

Let $G=(V, E)$ be a set of ordered set $W=\{W_1,W_2, W_3,...,W_k\}$ from the set of vertices in connected graph $G$. The metric dimension is the minimum cardinality of the resolving set on $G$. The representation of $v$ on $W$ is $k$ set. Vector $r(v|W)=(d(v, W_1), d(v, W_2), ...,$ $d(v, W_k))$ where $d(x, y)$ is the distance between the vertices $x$ and $y$. This study aims to determine the value of the metric dimensions and dimension of {\it non-isolated resolving set} on the wheel graph $(W_n)$. Results of this study shows that for $n \geq 7$, the value of the metric dimension and {\it non-isolated resolving set} wheel graph $(W_n)$ is $dim(W_n)=\lfloor \frac{n-1}{2} \rfloor$ and $nr(W_n)=\lfloor \frac{n+1}{2}\rfloor$. The first step is to determine the cardinality vertices and edges on the wheel graph, then determine $W$, with $W$ is the resolving set $G$ if {\it vertices} $G$ has a different representation. Next determine {\it non-isolated resolving set}, where $W$ on the wheel graph must have different representations of $W$ and all $x$ elements $W$ is connected in $W$.

Analisis Rainbow Vertex Connection pada Beberapa Graf Khusus dan Operasinya Ida Ariska; Dafik Dafik; Ika Hesti Agustin
CGANT JOURNAL OF MATHEMATICS AND APPLICATIONS Vol 2, No 1 (2021): CGANT JOURNAL OF MATHEMATICS AND APPLICATIONS
Publisher : jcgant

Suppose $G=(V(G),E(G))$ is a non-trivial connected graph with edge coloring defined as $c:E(G) \rightarrow \{1,2,...,k\} ,k \in N$, with the condition that neighboring edges can be the same color. An original path is {\it rainbow path} if there are no two edges in the path of the same color. The graph $G$ is called rainbow connected if every two vertices in $G$ with rainbow path in $G$. The coloring here is called rainbow coloring, and the minimal coloring in a graph $G$ rainbow connection number is denoted by $rc(G)$. Suppose $G=(V(G),E(G))$ is a non-trivial connected graph with a vertex coloring defined as $c':V(G) \rightarrow \{1,2,...,k\},k \in N$, with the condition that neighboring interior vertex may have the same color. An original path is rainbow vertex path if there are no two vertices in the path of the same color. The graph $G$ is called rainbow vertex connected if every two vertices in $G$ with rainbow vertex path in $G$. The $G$ coloring is called rainbow vertex coloring, and the minimal coloring in a $G$ graph is called rainbow vertex connection number which is denoted by $rvc(G)$. This research produces rainbow vertex connection number on the graph resulting from the operation \emph{amal}($Bt_{m}$, $v$, $n$), $Wd_{3,m}$ $\Box$ $ P_n$, $P_m$ $\odot$ $Wd_{3,n}$, $Wd_{3,m}$ $+$ $C_n$, and \emph{shack}($Bt_{m}$, $v $, $n$).

Pewarnaan Ketakteraturan Lokal Inklusif pada Keluarga Graf Pohon Tree Umi Azizah Anwar; Arika Indah Kristiana; Arif Fatahillah; Dafik Dafik; Ridho Alfarisi
CGANT JOURNAL OF MATHEMATICS AND APPLICATIONS Vol 2, No 1 (2021): CGANT JOURNAL OF MATHEMATICS AND APPLICATIONS
Publisher : jcgant

All graph in this paper is a simple and connected graph. We define $l: V(G) \to \{ 1, 2, 3,...k\} $ is called vertex irregular k-labeling and $w: (G) \to N$ the weight function with $[\sum_{u \epsilon N} l(u) + l(v) ]$. A local irregularity inclusive coloring if every $u, v \epsilon E(G), w(u) \ne w(v) $ and $max (l) = min \{ max (l_i), l_i label function\}$. The chromatic number of local irregularity inclusive coloring of $G$ denoted by $\chi_{lis}^{i}$, is the minimum cardinality of local irregularity inclusive coloring. We study about the local irregularity inclusive coloring of some family tree graph and we have found the exact value of their chromatic number.

Konstruksi Rak Penataan Gelas Air Minum Menggunakan Hasil Deformasi Benda-Benda Geometri dan Kurva Bezier Hikmah Ardiantika Sari; Bagus Juliyanto; Firdaus Ubaidillah
CGANT JOURNAL OF MATHEMATICS AND APPLICATIONS Vol 2, No 1 (2021): CGANT JOURNAL OF MATHEMATICS AND APPLICATIONS
Publisher : jcgant

Drinking water glass shelves are used as containers that can hold drinking water with a growing model. Drinking water glass shelves is made using thecniques which produced from deformation of geometric objects and Bezier curves. This research aims to made produces procedures for designing buffers, main shelves and more varied reliefs with one axis and three modeling axes. This research method divided into several stages. First, construct some basic objects as constituent components of drinking water glass shelves from deformation of octagonal, tube, beams, and the ball. Second, set some basic objects of the component of drinking water glass shelves two types of modeling axis. Third, arrange program using Maple 13. The results of this research obtained the procedure for designing various forms of constituent components of drinking water glass shelves from the basic object of a octagonal, tube, beams, and the ball. Furthermore, the procedure for assembling the components of drinking water glass from the first procedure result on two types of modeling axis.

Analisa Antimagicness Super dari Shackle Graf Parasut dan Aplikasinya pada Polyalphabetic Cipher Riza Nurfadila; Ika Hesti Agustin; Kusbudiono Kusbudiono
CGANT JOURNAL OF MATHEMATICS AND APPLICATIONS Vol 2, No 1 (2021): CGANT JOURNAL OF MATHEMATICS AND APPLICATIONS
Publisher : jcgant

Super (\emph{a,d})-$\mathcal{H}$-antimagic total covering on a graph \emph{G}=(\emph{V,E}) is the total labeling of $\lambda$ of \emph {V(G)} $\cup$ \emph{E(G)} with positive integers \{1, 2, 3,\dots ,$|V(G) \cup E(G)|$\}, for any subgraph \emph{H'} of \emph{G} that is isomorphic to \emph{H} where $\sum$ \emph{H'} = $\sum_{v \in V(H)} \lambda (v ) + \sum_{e \in E(H)} \lambda (e)$ is an arithmetic sequence \{\emph{a, a+d, a+2d,\dots,a+(s-1)d}\} where \emph{a}, \emph{d} are positive numbers where \emph{a} is the first term, \emph{d} is the difference, and \emph{s} is the number of covers. If $\lambda(v)_{v \in V} = {1,2,3,\dots,|V(G)|}$ then the graph \emph{G} have the label of super $\mathcal{H}$-antimagic covering. One of the techniques that can be applied to get the super antimagic total covering on the graph is the partition technique. Graph applications that can be developed for super antimagic total covering are \emph{ciphertext} and \emph{streamcipher}. \emph{Ciphertext} is an encrypted message and is related to cryptography. \emph{Stream cipher} is an extension of \emph{Ciphertext}. This article study the super (a,d)-$\mathcal{H}$-antimagic total covering on the shackle of parachute graph and its application in \emph{ciphertext}. The graphs that used in this article are some parachute graphs denoted by \emph{shack}($\mathcal{P}_{m},e,n$).

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Zainur Rasyid Ridlo

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cgant.unej@gmail.com

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+6285335111231

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cgant.unej@gmail.com

Editorial Address
Jl. Kalimantan Tegalboto No.37, Krajan Timur, Sumbersari, Kec. Sumbersari, Kabupaten Jember, Jawa Timur 68121

Location
Kab. jember,

Jawa timur

INDONESIA

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Abstract

Abstract

Home Page

OAI Link

Editorial Team

Contact

Reviewer

Google Scholar

Contact Name Zainur Rasyid Ridlo

Contact Email cgant.unej@gmail.com

Phone +6285335111231

Journal Mail Official cgant.unej@gmail.com

Editorial Address Jl. Kalimantan Tegalboto No.37, Krajan Timur, Sumbersari, Kec. Sumbersari, Kabupaten Jember, Jawa Timur 68121

Location Kab. jember, Jawa timur INDONESIA

Abstract

Abstract

Abstract

Abstract

Abstract

Abstract

Abstract

Abstract

Contact Name
Zainur Rasyid Ridlo

Contact Email
cgant.unej@gmail.com

Phone
+6285335111231

Journal Mail Official
cgant.unej@gmail.com

Editorial Address
Jl. Kalimantan Tegalboto No.37, Krajan Timur, Sumbersari, Kec. Sumbersari, Kabupaten Jember, Jawa Timur 68121

Location
Kab. jember,

Jawa timur

INDONESIA