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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 1, No 2 (2020): CGANT JOURNAL OF MATHEMATICS AND APPLICATIONS" : 8 Documents clear

Pewarnaan Titik r-Dinamis pada Graf Hasil Operasi Edge Corona Adelia Putri Liowardani; Dafik Dafik; Arif Fatahillah
CGANT JOURNAL OF MATHEMATICS AND APPLICATIONS Vol 1, No 2 (2020): CGANT JOURNAL OF MATHEMATICS AND APPLICATIONS
Publisher : jcgant

This research is a development of research on $r$-dynamic vertex coloring on simple, connected, and undirected graphs. The $r$dynamic vertex coloring on the graph $G$ is the $r$ point coloring of the $r$ graph so that the vertices of degree two on the $G$ graph have at least two different color neighbors. The $r$-dynamic vertex coloring is satisfied if it meets the conditions for $\forall v \in V(G)$, $|c(N(v))|$ $\geq$ min$\{r,d(v)\}$. The chromatic number for the $r$-dynamic vertex coloring of the graph $G$ is denoted as $\chi_r(G)$. In this study, we discuss the $r$-dynamic vertex coloring on the graph resulting from the \emph{edge corona} operation on a path graph with a complete graph, a star graph, and a sweep graph. It is denoted that the result of the operation of \emph{edge corona} graph $G$ and graph $H$ is $G \diamond H$. In this study, the results of the $r$-dynamic vertex coloring are described in the operation graph $P_n \diamond K_m$, $P_n \diamond S_m$, $P_n \diamond P_m$, and $P_n \diamond B_{(m,k)}

Analysis Creative Thinking Pattern on X Sains 2 at SMAN 2 Jember to Solving Open Ended Problem of Space and Shape Elsa Yuli Kurniawati; Dafik Dafik; Arif Fatahillah
CGANT JOURNAL OF MATHEMATICS AND APPLICATIONS Vol 1, No 2 (2020): CGANT JOURNAL OF MATHEMATICS AND APPLICATIONS
Publisher : jcgant

Math learning to train people to think critically, creatively, logical, analytical and systematic. In reality, mathematics is often regarded as the science that emphasizes logical thinking with a unique solution and certainly, so that students do not have the flexibility to develop creative ideas. The condition causes low creativity of students in learning mathematics. Curriculum 2006 stated that creative thinking skills needed to master the science of the future, given that today's science and technology is developing very rapidly \cite{BSNP}. Thus, the ability to think creatively is important to develop. This study describes the rate and the process of creative thinking class X IPA 2 SMA Negeri 2 Jember, in solving open ended problems. Instruments used in this research is to test the ability to think creatively package A and package B, questionnaires and interview guidelines. Of the 36 students of class X IPA 2 SMA Negeri 2 Jember included TBK 0 (not creative) as much as two students (5.56\%), TBK 1 (less creative) as many as twenty students (55.56\%), TBK 2 (enough creative) thirteen students (36.1\%), TBK 3 (creative) only one student (2.78\%) and no students were able to achieve TBK 4 (very creative). Because there are only four levels of creative thinking then taken four students as research subjects who identified the creative thinking process. Students TBK 3 very fulfilling to aspects of fluency and flexibility aspects, but for the novelty aspect is still lacking. Students TBK 2 only meet the flexibility aspect alone. Students TBK 1 which fulfills the eloquence alone. Students who do not meet the TBK 0 fluency aspect, the aspect of flexibility and novelty aspect.

Bilangan Kromatik Graceful pada Keluarga Graf Unicyclic Nafisa Afwa Sania; Dafik Dafik; Arif Fatahillah
CGANT JOURNAL OF MATHEMATICS AND APPLICATIONS Vol 1, No 2 (2020): CGANT JOURNAL OF MATHEMATICS AND APPLICATIONS
Publisher : jcgant

Suppose $ G $ is a graph, where $ G = \{V (G), E (G) \} $. Graceful coloring is defined by $ c: V (G) \to \{1,2, ..., k \} $ which induces a proper edge coloring $ c': E (G) \to \{1,2, ..., k- 1 \}$ defined by $c'(xy)=|c(x)-c(y)|$, where $ k \geq 2 $, $ k \in N $. Coloring is said to be graceful if these 3 conditions are satisfied, namely the proper vertex color, the proper edge color, and the edge color, which are the absolute difference between the color of the accident vertex. The subgraph $H$ on that graceful coloring is smaller than the $G$. Furthermore, one of the subgraphs in the unicyclic graph family is a cycle graph. The graceful chromatic number on a graph denoted by $ \chi_g (G) $, is the optimum number of graceful colors from graph $G$. This research aims to find graceful chromatic numbers in the unicyclic graph family, namely bull graphs, net graphs, cricket graphs, caveman graphs, peach graphs, and flowerpot graphs. The results of this study indicate that $\chi_g(C_l) \geq 4$, where $C_l$ is a unicyclic graphs.

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} $.

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.

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.

Pengembangan Affine Chiper dalam Pelabelan Super Antiajaib Graf Buku Bersusun Menggunakan Pemrograman Matlab Vutikatul Nur Rohmah; Dafik Dafik; Arif Fatahillah
CGANT JOURNAL OF MATHEMATICS AND APPLICATIONS Vol 1, No 2 (2020): CGANT JOURNAL OF MATHEMATICS AND APPLICATIONS
Publisher : jcgant

Super $(a, d)-\mathcal{H}-$ antimagic total covering labeling on a graph $G=(V,E)$ is total labelling $\lambda$ on $V(G)UE(G)$ to set integers $\{1,2,3,..., |V(G)UE(G)|\}$ form an arithmetic sequence $\{a, a+d, a+2d, . . .,a+(s-1)d\}$ where $a, d$ are positive integer with $a$ is firt integer, $d$ is different, and $s$ is sum of covering. This research purposes to determine cardinality of vertex, cardinality of edge, upper limit of difference value, difference value from shackle of stacked book graph.The first step is determine cardinality of vertex and cardinality of edge on shackle of stacked book graph. Then determine upperlimit if difference value and the partition from labeling on shackle of stacked book graph. So that be produced super $(a, d)-\mathcal{H}-$antimagic total covering labeling on shackle of stacked book

Dimensi Metrik Sisi Pada Beberapa Graf Unicyclic Bayu Aprilianto; 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 the graphs in this paper are connected graphs and $d(e,v)$ is the length of the shortest path between $e=uv$ and $v$. 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 $G$. The edge metric dimension is a topic that is closely related to the cardinality of the distance of each edge on the graph $G$ with respect to the resolving set $W$ which is denoted by $dim_E(G)$. Let if the subset of vertex $W=\{w_1,w_2,w_3,...,$ $w_k\}$, then the representation of the distance of the $uv$ edge to the set of differences is k-tuple $r(uv|W)=(d(uv,w_1),d(uv,w_2),d(uv,w_3),...,d(uv,w_k)$. A unicyclic graph is one that only has exactly one cycle. In this paper, we will study edge metric dimensions on some families of unicyclic graphs.

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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

Abstract

Abstract

Abstract

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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

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