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All Journal International Journal of Electrical and Computer Engineering Jurnal Ilmu Dasar Jurnal Edukasi Universitas Jember KADIKMA CAUCHY: Jurnal Matematika Murni dan Aplikasi Tadris: Jurnal keguruan dan Ilmu Tarbiyah Saintifika Prosiding Seminar Matematika dan Pendidikan Matematik UNEJ e-Proceeding Al-Jabar : Jurnal Pendidikan Matematika BAREKENG: Jurnal Ilmu Matematika dan Terapan Indonesian Journal of Combinatorics Al-Khwarizmi: Jurnal Pendidikan Matematika dan Ilmu Pengetahuan Alam Jurnal Riset Pendidikan dan Inovasi Pembelajaran Matematika (JRPIPM) Alifmatika: Jurnal Pendidikan dan Pembelajaran Matematika CGANT JOURNAL OF MATHEMATICS AND APPLICATIONS Pancaran Pendidikan SAINTIFIKA

D. Dafik

Universitas Jember, Indonesia

Author-ID : 488491

Religion Agriculture, Biological Sciences & Forestry Humanities Biochemistry, Genetics & Molecular Biology Chemical Engineering, Chemistry & Bioengineering Chemistry Computer Science & IT Control & Systems Engineering Decision Sciences, Operations Research & Management Economics, Econometrics & Finance Education Electrical & Electronics Engineering Energy Engineering Health Professions Languange, Linguistic, Communication & Media Mathematics Mechanical Engineering Medicine & Pharmacology Physics Social Sciences Transportation Other

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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.

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 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 $\chi(G)$.

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.

Co-Authors A Arynda A H Rahmatillah A. Y. Harsya Adelia Putri Liowardani Adelia Putri Liowardani Agnes Ika Nurvitaningrum, Agnes Ika Agrita Kanty Purnapraja, Agrita Kanty Agustina M. Agustina Muharromah, Agustina Ahmad Adi Ahmad Musyaffa' Hikamuddin Ahmad Syaiful Rizal, Ahmad Syaiful Aldyon Restu Azkarahman Alfian Yulia Harsya, Alfian Yulia Alfin Nabila Taufik Amalina, Putri Nur Anindyta Anggirena Wulandari Anindyta Anggirena Wulandari Anisa Meilinda Wardani Antonius C. Prihandoko arief fatahillah Arika I. Kristiana Arika Indah Kriatiana Arika Indah Kristiana Arnasyitha Yulianti S, Arnasyitha Arnasyitha Yulianti Soelistya Artanty Nastiti, Artanty Bayu Aprilianto Darian Aji Bawono Desak Made Dwika Saniriati Desi Febriani Putri Desi Febriani Putri Desy Tri Puspasari Desy Tri Puspasari, Desy Tri Devi Eka Wardani M, Devi Eka Dewi Anggraeni Dewi ANGGRAENI Dian Anita Hadi Dian Anita Hadi, Dian Anita Didik Sugeng Didin Trisnani, Didin Dina Tri Djoni Budi Sumarno Dwi Agustin Retnowardani Dyna Probo Mukti Elitta P Dewy Elok Asmaul Husna Elok Asmaul Husna Elsa Yuli Kurniawati Elsa Yuli Kurniawati Elsy Wijayanti Elsy Wijayanti Endang Wahyuningrum Ermita R Albirri Ermita Rizki Albirri Ervin Eka Riastutik Ervin Eka Riastutik, Ervin Eka Ervin Oktavianingtyas Erwinda Viantasari Excelsa Suli Wildhatul Jannah Farah Rezita Nurtaatti, Farah Rezita Fathulloh Faruq Fia Cholidah, Fia Firman Firman Fitri Wulandari Fitri Wulandari Gembong A. W. Hani'ah Zakin Harianto Setiawan, Harianto Hendry Dwi Saputro Herninda Lucky Oktaviana Hilmiyah Hanani Hilmiyah Hanani Hobri I H Agustin I H. Agustin I Ikhwandi I M Tirta I Made Tirta Ida Ariska Ika Hesti A. Ika Hesti Agustin, Ika Hesti Ika Mareta Ika Nur Maylisa Imanul Umar Hawari Imro’atun Rofikah Indar Setiani Indi Izzah Makhfduloh Inge Yosanda Arianti, Inge Yosanda Irma Azizah Irma Azizah, Irma Istamala Idha Retnoningsih Jackson P Mairing Jamhari Jamhari Jesi Irwanto, Jesi Joni Susanto Joni Susanto, Joni Juanda Brahmanto K Kasturi K Khasan, K Karinda Rizqy Aprilia, Karinda Rizqy Khilyah Munawaroh Kholifatu Rosyidah Kholifatur Rosyidah Kiki Kurdianto Kiswara Agung Santoso Kurniawati, Elsa Yuli Kusbudiono Kusbudiono, Kusbudiono Laily Anisa Nurhidayati Laily Anisa Nurhidayati Lubis Muzaki Lusia Dewi Minarti Lusia Dewi Minarti M. Wildan Athoillah Marsidi Marsidi Miftahur Roifah Millatuz Zahroh, Millatuz Moch. Avel Romanza P Moch. Avel Romanza P, Moch. Avel Romanza Mohammad Fadli Rahman Mohammad Fadli Rahman Muhamad Faizal Fatoni Muhammad Lutfi Asy’ari Muhlisatul Mahmudah Muhlisatul Mahmudah, Muhlisatul N Maylisa N Y. Sari Nabilah Ayu Az-Zahra Nafisa Afwa Sania Nindya Laksmita Dewi, Nindya Laksmita Novalita Anjelia Novalita Anjelia Novian Nur Fatihah Novita Cahya Mahendra Novita Sana Susanti Novri Anggraeni, Novri Nur Alfiyantiningsih Nur Asia Jamil, Nur Asia Nurcholif Diah Sri Lestari Nuris Hisan Nazula Nuryatul Laili Nuwaila Izzatul Muttaqi O A Safiati O. A. Safiati Ojat Darojat Okti Anis Safiati Prihandini, Rafiantika Megahnia Putri Ayu Permatasari Putri Indah Pratiwi Putri Rizky H.P, Putri Rizky Putu Liana Wardani Q Qoriatul QurrotaAÃ¢Â€Â™yuniArRuhimat AÃ¢Â€Â™yuni ArRuhimat QurrotaA’yuniArRuhimat A’yuni ArRuhimat Qurrotul A’yun Quthrotul Aini Fuidah R Adawiyah R M Prihandini R Ratih R Rohmatullah R. Humaizah Rafiantika M Rafiantika Megahnia Prihandini Randhi N. Darmawan, Randhi N. Randi Pratama Murtikusuma Ratna Syafitri Ratna Syafitri Reza Mega Ardhilia Ridho Alfarisi Ridho Alfarisi, Ridho Riniatul Nur Wahidah Rizki Aulia Akbar Robiatul Adawiyah Robiatul Adawiyah Robiatul Adawiyah Robiatul Adawiyah Rukmana Sholehah Rukmana Sholehah, Rukmana S Slamin S Suciati S Suharto S Sunardi S Susanto S Susanto S Susanto S Susanto S. Chususiyah S. M. Yunika Saddam Hussen Safira Izza Ghafrina Safira Izza Ghafrina Saifudin, Ilham Saniriati, Desak Made Dwika Shapbian Novindasari Shapbian Novindasari, Shapbian Shela Okta Grefina, Shela Okta Sherly Citra Wuni, Sherly Citra Sih Muhni Yunika, Sih Muhni Siska Aprilia Hardiyanti Siska Binastuti Siska Binastuti, Siska Siswono, Hendrik Siti Aminatus Solehah Siti Latifah Siti MarÃ¢Â€Â™atus Sholihah Siti Mar’atus Sholihah Soleh Chudin Sri Tresnaningsih Sufirman Sufirman Suntusia Suntusia Suparti Supratiningsih Supratiningsih Susanto Susanto Susanto Susanto Susi Setiawani Tanti Windartini, Tanti Tasrip Rudiono Tito Putra Mahendratama Sasongko Tommi Sanjaya Putra Toto Bara Setiawan Tri Dyah Prastiti Ulul Azmi Umi Azizah Anwar Viqedina Rizky Noviyanti Vutikatul Nur Rohmah Wahyu Nikmatus Sholihah Wahyu Sulistio Weny Wijayanti Weny Wijayanti, Weny Wicha Dwi Wicha Dwi Vikade, Wicha Dwi Y Yunita Yessy Eki Fajar Reksi Yuli Nur Azizah, Yuli Nur Z R Ridlo Zainur Rasyid Ridlo

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