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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 52 Documents

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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 Locating Dominating Set pada Graf Khusus dan Hasil Operasi Comb Sisi Imro’atun Rofikah; Ika Hesti Agustin; Dafik Dafik
CGANT JOURNAL OF MATHEMATICS AND APPLICATIONS Vol 1, No 2 (2020): CGANT JOURNAL OF MATHEMATICS AND APPLICATIONS
Publisher : jcgant

Assume that G = (V;E) is an undirected and connected graph with vertex set V and edge set E. D is called a dominating set of the vertex in G such that for each vertex v 2 V one of: v 2 D or a neighbor u of v in D with u 2 D. While locating dominating set of G is a dominating set D of G when satisfy this condition: for every two vertices u; v 2 (V ???? D);N(u) \ DN(v) \ D. The minimum cardinality of a locating dominating set of G is the location domination number L(G). In this paper, locating dominating set and location domination number of special graph and edge comb product operation result will be determined. Location domination number theorem on triangular book graph Btn and edge comb product operation result that is Cm D Btn and Sm D Btn are the results from this experiment.

On r-Dynamic Coloring for Graph Operation of Cycle, Star, Complete, and Path Desy Tri Puspasari; Dafik Dafik; Slamin Slamin
CGANT JOURNAL OF MATHEMATICS AND APPLICATIONS Vol 1, No 1 (2020): CGANT JOURNAL OF MATHEMATICS AND APPLICATIONS
Publisher : jcgant

For integer k, r > 0, (k, r) -coloring of graph G is a proper coloring on the vertices of G by k-colors such that every vertex v of degree d(v) is adjacent to vertices with at least min{d(v), r} diﬀerent color. By a proper k -coloring of graph G, we mean a map c : V (G) → S, where |S| = k, such that any two adjacent vertices are diﬀerent color. An r -dynamic k -coloring is a proper k -coloring c of G such that |c(N (v))| ≥ min{r, d(v)} for each vertex v in V (G), where N (v) is the neighborhood of v and c(S) = {c(v) : v ∈ S} for a vertex subset S . The r-dynamic chromatic number, written as χr (G), is the minimum k such that G has an r-dynamic k-coloring. Note the 1-dynamic chromatic number of graph is equal to its chromatic number, denoted by χ(G), and the 2-dynamic chromatic number of graph denoted by χd (G). By simple observation with a greedy coloring algorithm, it is easy to see that χr (G) ≤ χr+1(G), however χr+1(G) − χr (G) does not always have the same diﬀerence. Thus finding an exact values of χr (G) is significantly useful. In this paper, we investigate the some exact value of χr (G) when G is for an operation product of cycle, star, complete, and path graphs.

Analisis Gelombang Air Laut dengan Menggunakan Pemodelan Berbasis Matlab Zainur Rasyid Ridlo; Luthfin Afafa; Efrika Marsya Ulfa; Mawardani Adi Pratama Dewi; Siti Maimuna
CGANT JOURNAL OF MATHEMATICS AND APPLICATIONS Vol 2, No 2 (2021): CGANT JOURNAL OF MATHEMATICS AND APPLICATIONS
Publisher : jcgant

Waves are the propagation of energy from one place to another without dragging the material in its path. The waves on Papuma Beach are classified as technical waves because they require a medium to propagate and transfer the required energy. When the waves move at a certain height, the waves on Papuma Beach have a potential force. This potential force depends on the height of an object. When the waves on Papuma Beach get higher, it also has high potential energy. The method used in this research is the analysis of physical concepts related to the indigenous. Research method of analyzing the concept of physics, analyze the formulas and quantities used coding the MATLAB for making illustrations and to calculate the formulas. Potential energy is formulated with. The energy in the waves is a combination of kinetic energy and potential energyand thanproduce the formula.

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 $, $n$).

Resolving Domination Number pada Keluarga Graf Buku Quthrotul Aini Fuidah; Dafik Dafik; Ermita Rizki Albirri
CGANT JOURNAL OF MATHEMATICS AND APPLICATIONS Vol 1, No 2 (2020): CGANT JOURNAL OF MATHEMATICS AND APPLICATIONS
Publisher : jcgant

All graph in this paper are members of family of book graph. Let $G$ is a connnected graph, and let $W = \{w_1,w_2,...,w_i\}$ a set of vertices which is dominating the other vertices which are not element of $W$, and the elements of $W$ has a different representations, so $W$ is called resolving dominating set. The minimum cardinality of resolving dominating set is called resolving domination number, denoted by $\gamma_r(G)$. In this paper we obtain the exact values of resolving dominating for family of book graph.

Analysis Super (a; d)-S3 Antimagic Total Dekomposition of Helm Graph Connektive for Developing Ciphertext Kholifatur Rosyidah; Dafik Dafik; Susi Setiawani
CGANT JOURNAL OF MATHEMATICS AND APPLICATIONS Vol 1, No 1 (2020): CGANT JOURNAL OF MATHEMATICS AND APPLICATIONS
Publisher : jcgant

Covering of G is H = fH1; H2; H3; :::; Hkg subgraph family from G with every edges on G admit on at least one graph Hi for a i 2 f1; 2; :::; kg. If every i 2 f1; 2; :::; k g, Hi isomorphic with a subgraph H, then H said cover-H of G. Furthermore, if cover-H of G have a properties is every edges G contained on exactly one graph Hi for a i 2 f1; 2; :::; kg, then cover-H is called decomposition-H. In this case, G is said to contain decomposition-H. A graph G(V; E) is called (a; d)-H total decomposition if every edges E is sub graph of G isomorphic of H. In this research will be analysis of super (a; d)-S3 total decomposition of connective helm graph to developing ciphertext.Key Word : Super (a; d)-S3, Dekomposisi, Graf helm, dan Ciphertext

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

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 $\chi(G)$.

Analisis Rainbow Antimagic Coloring Pada Hasil Operasi Comb Graf Lintasan Feby Suryandana
CGANT JOURNAL OF MATHEMATICS AND APPLICATIONS Vol 2, No 2 (2021): CGANT JOURNAL OF MATHEMATICS AND APPLICATIONS
Publisher : jcgant

All the graphs in this paper are connected graphs. Let $G=(V,E)$ where $V(G)$ is a set of vertex from graph $G$ while $E(G)$ is a set of edge from graph $G$. A bijection function $f: V \rightarrow \{1,2,3,...,\lvert V(G)\rvert\}$ the associated weight of an edge $uv \in E(G)$ under $f$ is $W_f{(uv)}=f(u)+f(v)$. A path $P$ in a vertex-labeled graph $G$ is said to be a rainbow path if for every two edges $uv$, $u'v' \in E(P)$, there is $w_f{(uv)}\neq w_f{u'v'}$. If for every two vertices $u$ and $v$ of $G$, there is a rainbow $u$-$v$ path, then $f$ is called a rainbow antimagic labeling of $G$. A graph $G$ is rainbow antimagic if $G$ has a rainbow antimagic labeling. The minimum number of color needed to make $G$ rainbow connected, called rainbow antimagic connection number, denoted by rac(G). In this paper, we will analyze the rainbow antimagic coloring on comb product of path graph.

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.

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Zainur Rasyid Ridlo

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cgant.unej@gmail.com

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

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Kab. jember,

Jawa timur

INDONESIA

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Abstract

Abstract

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

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