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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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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

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.

Kajian Rainbow 2-Connected Pada Graf Eksponensial dan Beberapa Operasi Graf Herninda Lucky Oktaviana; Ika Hesti Agustin; Dafik Dafik
CGANT JOURNAL OF MATHEMATICS AND APPLICATIONS Vol 2, No 2 (2021): CGANT JOURNAL OF MATHEMATICS AND APPLICATIONS
Publisher : jcgant

Let $G=(V(G),E(G))$ is a graph connected non-trivial. \textit{Rainbow connection} is edge coloring on the graph defined as $f:E(G)\rightarrow \{1,2,...,r|r \in N\}$, for every two distinct vertices in $G$ have at least one \textit{rainbow path}. The graph $G$ says \textit{rainbow connected} if every two vertices are different in $G$ associated with \textit{rainbow path}. A path $u-v$ in $G$ says \textit{rainbow path} if there are no two edges in the trajectory of the same color. The edge coloring sisi cause $G$ to be \textit{rainbow connected} called \textit{rainbow coloring}. Minimum coloring in a graph $G$ called \textit{rainbow connection number} which is denoted by $rc(G)$. If the graph $G$ has at least two \textit{disjoint rainbow path} connecting two distinct vertices in $G$. So graph $G$ is called \textit{rainbow 2-connected} which is denoted by $rc_2(G)$. The purpose of this research is to determine \textit{rainbow 2-connected} of some resulting graph operations. This research study \textit{rainbow 2-connected} on the graph (${C_4}^{K_n}$ and $Wd_{(3,2)}\square K_n$).

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 $shack(H_{2,2},v,n)$.

Dominating Set of Operation of Special Graphs Hendry Dwi Saputro; Ika Hesti A.; Dafik Dafik
CGANT JOURNAL OF MATHEMATICS AND APPLICATIONS Vol 1, No 1 (2020): CGANT JOURNAL OF MATHEMATICS AND APPLICATIONS
Publisher : jcgant

A set D of vertices of a simple graph G, that is a graph without loops and multiple edges, is called a dominating set if every vertex u 2 V (G) D is adja-cent to some vertex v 2 D. The domination number of a graph G, denoted by (G), is the order of a smallest dominating set of G. A dominating set D with jDj = (G) is called a minimum dominating set. We will show dominating set of graph operation of special graph (Pn, Km, cycle Cn, Wm, ladder Ln, Btm, and special graph G1, G2.

Nilai Ketidakteraturan Total Selimut pada Graf Yessy Eki Fajar Reksi; Dafik Dafik; Ika Hesti Agustin
CGANT JOURNAL OF MATHEMATICS AND APPLICATIONS Vol 2, No 2 (2021): CGANT JOURNAL OF MATHEMATICS AND APPLICATIONS
Publisher : jcgant

Misal $G$ dan $K$ adalah graf sederhana, nontrivial dan graf tak berarah. Operasi \emph{total comb product} menghasilkan graf baru dengan mengoperasikan dua buah graf. Misalkan \emph{G} dan \emph{K} adalah graf terhubung dan \emph{v} $\in$ \emph{V(K}) dan \emph{e} $ \in $ \emph{E(K)}. Operasi \emph{total comb product} dari graf \emph{G} dan \emph{K} yang dinotasikan ($G$ $\dot{\unrhd}$ $K$) merupakan operasi graf yang diperoleh dengan mengambil salinan satu graf \emph{G} dan $|V(G)|+|E(G)|$ salinan \emph{K}, kemudian merekatkan salinan ke-\emph{i} dari graf \emph{K} di titik cangkok \emph{v} pada titik ke-\emph{i} dari graf \emph{G} dan merekatkan salinan ke-\emph{j} dari graf \emph{K} di sisi cangkok \emph{e} pada sisi ke-\emph{j} dari graf \emph{G}. Pelabelan total didefinisikan suatu fungsi $f : V(G) \cup E(G) \rightarrow \{1,2,3,...,k\}$ merupakan pelabelan \emph{k-total} pada graf $G$. Pelabelan \emph{k-total} dikatakan pelabelan total ketidakteraturan selimut pada graf $G$ jika untuk $H \subseteq G$ dengan kata lain $H$ merupakan selimut dari suatu graf $G$, bobot total selimut $W(H)=\Sigma_{v\in V(H)}f(v)+\Sigma_{e\in E(H)}f(e)$ berbeda. Nilai minimum $k$ pada pelabelan total ketidakteraturan selimut disebut dengan \emph{total H-Irregularity Strength} dari suatu graf $G$ yang dinotasikan dengan $tHs(G)$. Pada artikel ini dilakukan penelitian tentang pelabelan total ketidakteraturan selimut yaitu mencari nilai ketidakteraturan total selimut pada graf hasil operasi \emph{total comb product} dari graf khusus.

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.

Dimensi Metrik Ketetanggaan Lokal pada Graf Hasil Operasi Korona G odot P_3 dan G odot S_4 Alfin Nabila Taufik; Dafik Dafik; Rafiantika Megahnia Prihandini; Ridho Alfarisi
CGANT JOURNAL OF MATHEMATICS AND APPLICATIONS Vol 1, No 2 (2020): CGANT JOURNAL OF MATHEMATICS AND APPLICATIONS
Publisher : jcgant

There are variant of the metric dimensions in graph theory, one of them is a local adjacency metric dimension. Let $W\subset V(G)$ with $W=\{w_1,w_2,\dots,w_k\}$, the representation of the vertex $V\in V(G)$, $r_A(v|W)=(d_A(v,w_1),d_A(v,w_2),\dots,d_A(v,w_k))$ with $ d_ {A} (v, w) $= $ 0 $ if $ v = w $, $ d_ {A} (v, w) $= $ 1 $ if $ v$ adjacent to $w $, and $ d_ {A} (v, w) $ =$ 2 $ if $ v $ does not adjacent to $ w $. If every two adjacent vertices $ v_1 $, $ v_2 \in V (G) $, $ r_ {A} (v_1 | W) \neq r_ {A} (v_2 | W) $, then $W$ is the minimum cardinality of the local adjacency metric dimension. The minimum cardinality of $W$ is called the local adjacency metric dimension number, denoted by $ \dim_{(A, l)} (G) $. In this paper, we have found the local adjacency metric dimension of corona product of special graphs, namely the $ L_n \odot {P_3} $ graph, $ S_n \odot {P_3} $ graph, $ C_n \odot {P_3} $ graph, $ P_n \odot {S_4} $ graph, and the graph $ L_n \odot {S_4} $.

Independent Domination Number of Operation Graph Siti Aminatus Solehah; Ika Hesti Agustin; Dafik Dafik
CGANT JOURNAL OF MATHEMATICS AND APPLICATIONS Vol 1, No 1 (2020): CGANT JOURNAL OF MATHEMATICS AND APPLICATIONS
Publisher : jcgant

Let G be a simple, undirected and connected graph. An independent set or stable set is a set of vertices in a graph in which no two of vertices are adjacent. A set D of vertices of graph G is called a dominating set if every vertex u ∈ V (G) − D is adjacent to some vertex v ∈ D. A set S of vertices in a graph G is an independent dominating set of G if S is an independent set and every vertex not in S is adjacent to a vertex in S. A minimum independent dominating set is an independent set of smallest possible size for a given graph G. This size is called the independence number of G, and denoted i(G). Operation Graph is a technical to get a new graph types by performing the operation of two or more graphs. Power Graph is a operation graph where let the graph G and H , notation of the power graph is (GH ). Keywords: r-dynamic coloring, r-dynamic chromatic number, graph operations.

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

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 Ketakteraturan Lokal pada Keluarga Graf Unicyclic Khilyah Munawaroh; Arika Indah Kristiana; Ermita Rizki Albirri; Dafik Dafik; Robiatul Adawiyah
CGANT JOURNAL OF MATHEMATICS AND APPLICATIONS Vol 2, No 2 (2021): CGANT JOURNAL OF MATHEMATICS AND APPLICATIONS
Publisher : jcgant

In this research is a development of local irregularity vertex coloring of graph. The based on definition, as follows: \textbf{$l:V(G) \longrightarrow {\{1, 2, ..., k}\}$} is called vertex irregular k-labelling and \textbf{$w:V(G) \longrightarrow N$} where \textbf{$w(u) = \varSigma_{ v \in N(u)}l(v)$}, $w$ is called local irregularity vertex coloring. A condition for $w$ to be a local irregularity vertex coloring, If \textit{opt$(l)$ = min\{maks$(li); li$, vertex labelling function}, and for every \textbf{$u,v\in E(G),w(u)\ne w(v)$}. The chromatic number local irregularity vertex coloring is denoted by $\chi_{lis}(G)$. In this paper, the researchers will discuss of local irregularity vertex coloring of related unicyclic graphs and we have found the exact value of their chromatic number local irregularity, namely cricket graph, net graph, tadpole graph, \textit{peach} graph, and bull graph.

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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