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Super (a; d) - Face Antimagic Total Labeling of Connective Shackle Graph (C5; e; n) Siska Binastuti; Dafik Dafik; Arif Fatahillah
CGANT JOURNAL OF MATHEMATICS AND APPLICATIONS Vol 1, No 1 (2020): CGANT JOURNAL OF MATHEMATICS AND APPLICATIONS
Publisher : jcgant

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (2425.018 KB) | DOI: 10.25037/cgantjma.v1i1.5

Abstract

Let G be a simple graph of order p, size q and face r. The graph G is called a super (a; d) - face antimagic total labeling , if there exist a bijection f : V (G) [ E(G) [ F (G) ! f1; 2; :::; p + q + rg such that the set of s-sided face weights, Ws = fas; as + d; as + 2d; :::; as + (rs ¡1)dg form an arithmetic sequence with ¯rst term a,common di®erence d, where a and d are positive integers s and rs is the number of s-sided faces. Such a graph is called super if the smallest possible labels appear on the vertices. The type of Face Antimagic Labeling is (1,1,1). In this paper, describe of Super (a; d) - Face Antimagic of Connective Shackle (C5; e; n) Graph. Keywords: Super (a; d)-face antimagic total labeling, face antimagic la-beling.
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
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Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (690.435 KB) | DOI: 10.25037/cgantjma.v3i1.72

Abstract

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
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Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (1460.907 KB) | DOI: 10.25037/cgantjma.v2i2.56

Abstract

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
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Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (411.773 KB) | DOI: 10.25037/cgantjma.v2i1.47

Abstract

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
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Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (1663.028 KB) | DOI: 10.25037/cgantjma.v1i1.11

Abstract

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
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Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (649.521 KB) | DOI: 10.25037/cgantjma.v2i2.67

Abstract

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
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Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (567.237 KB) | DOI: 10.25037/cgantjma.v2i1.52

Abstract

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
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Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (350.338 KB) | DOI: 10.25037/cgantjma.v1i2.43

Abstract

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

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (976.66 KB) | DOI: 10.25037/cgantjma.v1i1.6

Abstract

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
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Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (645.265 KB) | DOI: 10.25037/cgantjma.v3i1.73

Abstract

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.
Co-Authors A Arynda A H Rahmatillah A. Y. Harsya Adawiyah, R 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 Futuhul Hadi Alfian Yulia Harsya, Alfian Yulia Alfin Nabila Taufik Alfiyantiningsih, Nur Amalina, Putri Nur Anindyta Anggirena Wulandari Anisa Meilinda Wardani Annadhifi, Muhammad Ilham Nurfaizi Antonius Cahya Prihandoko Arif Fatahillah Arika I. Kristiana Arika Indah Kriatiana Arika Indah Kristiana Arnasyitha Yulianti S, Arnasyitha Arnasyitha Yulianti Soelistya ArRuhimat, QurrotaA’yuniArRuhimat A’yuni Artanty Nastiti, Artanty Asari, Okta Endri Asy’ari, Muhammad Lutfi Awalin, Qonita Ilmi Aziza, Adinda Putri A’yun, Qurrotul Bawono, Darian Aji Bayu Aprilianto Brahmanto, Juanda Cangul, Ismail Naci 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 Dewy, Elitta P Dian Anita Hadi, Dian Anita Didik Sugeng Didin Trisnani, Didin Dina Tri Djoni Budi Sumarno Dliou, Kamal Dwi Agustin Retnowardani Dyna Probo Mukti Elok Asmaul Husna Elsa Yuli Kurniawati Elsa Yuli Kurniawati Endang Wahyuningrum Ermita R Albirri Ermita Rizki Albirri Ervin Eka Riastutik, Ervin Eka Ervin Oktavianingtyas Excelsa Suli Wildhatul Jannah Farah Rezita Nurtaatti, Farah Rezita Faruq, Fathulloh fatahillah, arief Fatoni, Muhamad Faizal Fia Cholidah, Fia Firdausiyah, Iftitahul Firman Firman Fitri Wulandari Gembong A. W. Hani'ah Zakin Harianto Setiawan, Harianto Hendry Dwi Saputro Herninda Lucky Oktaviana Hilmiyah Hanani Hobri Husain, Sharifah Kartini Said I H Agustin I H. Agustin I Ikhwandi I M Tirta I Made Tirta I Made Tirta Ida Ariska Ika Hesti A. Ika Hesti Agustin, Ika Hesti Ika Mareta 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 Jannah, Excelsa Suli Wildhatul Jesi Irwanto, Jesi Joni Susanto, Joni K Kasturi K Khasan, K Karinda Rizqy Aprilia, Karinda Rizqy Khilyah Munawaroh Kholifatu Rosyidah Kholifatur Rosyidah Khusnul, Agustina Hotimatus Kiki Kurdianto Kiswara Agung Santoso Kurniawati, Elsa Yuli Kusbudiono Kusbudiono, Kusbudiono Laili, Nuryatul Laily Anisa Nurhidayati Liliek Susilowati Liowardani, Adelia Putri Lubis Muzaki Lusia Dewi Minarti Lusia Dewi Minarti M. Wildan Athoillah Makhfudloh, I I Mardiyah, Fitriyatul Marsidi Marsidi Maylisa, Ika Nur Miftahur Roifah Millatuz Zahroh, Millatuz Moch. Avel Romanza P, Moch. Avel Romanza Mohammad Fadli Rahman Mohanapriya, N. Muhammad Lutfi Asy’ari Muhlisatul Mahmudah, Muhlisatul Mursyidah, Indah Lutfiyatul Murtini Murtini, Murtini N Maylisa N Y. Sari Nabilah Ayu Az-Zahra Nafisa Afwa Sania Nindya Laksmita Dewi, Nindya Laksmita 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 Nuwaila Izzatul Muttaqi O A Safiati O. A. Safiati Ojat Darojat Okti Anis Safiati Permatasari, Putri Ayu Pratiwi, Putri Indah Prihandini, R M Prihandini, Rafiantika Megahnia Prihandini, Rafiantika Megahniah Prihandini, RM Prihandoko, AC Prof. Dr.I Nengah Suparta,M.Si . Pujiyanto, Arif Putra Mahendratama Sasongko, Tito Putri Rizky H.P, Putri Rizky Q Qoriatul QurrotaA’yuniArRuhimat A’yuni ArRuhimat Qurrotul A’yun Quthrotul Aini Fuidah R M Prihandini R Ratih R Rohmatullah R. Humaizah Rafiantika M Rafiantika Megahnia Prihandini Rahmadani, M R Rahman, Md. Saidur Randhi N. Darmawan, Randhi N. Randi Pratama Murtikusuma Ratna Syafitri Reza Mega Ardhilia Ridho Alfarisi Ridho Alfarisi, Ridho Ridlo, Zainur Rasyid Riniatul Nur Wahidah Rizki Aulia Akbar Robiatul Adawiyah Robiatul Adawiyah Robiatul Adawiyah Rohini, A Rukmana Sholehah, Rukmana S Slamin S Suciati S Suharto S Sunardi S Susanto S. Chususiyah S. M. Yunika Saddam Hussen Safira Izza Ghafrina Safira Izza Ghafrina Saifudin, Ilham Saniriati, Desak Made Dwika Santoso, Aji Mansur Septory, Brian Juned Shapbian Novindasari, Shapbian Shela Okta Grefina, Shela Okta Sherly Citra Wuni, Sherly Citra Sholihah, Siti Mar’atus Sih Muhni Yunika, Sih Muhni Siska Aprilia Hardiyanti Siska Binastuti Siska Binastuti, Siska Siswono, Hendrik Siti Aminatus Solehah Siti Latifah Siti Mar’atus Sholihah Soleh Chudin Sri Tresnaningsih Sufirman Sufirman Sulistio, Wahyu Sullystiawati, Lusia Herni Sunder, R. Suntusia Suntusia Suparti Supratiningsih Supratiningsih Susanto Susanto Susanto Susanto Susi Setiawani Tanti Windartini, Tanti Tasrip Rudiono Thoyibah, Fifi Tommi Sanjaya Putra Toto Bara Setiawan Tri Dyah Prastiti Ulul Azmi Umi Azizah Anwar Venkatachalam, M. Viantasari, Erwinda Viqedina Rizky Noviyanti Vutikatul Nur Rohmah Wahidah, Riniatul Nur Wahyu Lestari Wahyu Nikmatus Sholihah Wardani, Putu Liana Weny Wijayanti, Weny Wicha Dwi Wicha Dwi Vikade, Wicha Dwi WIHARDJO, EDY Wijayanti, Elsy Y Yunita Yanuarsih, Elly Yessy Eki Fajar Reksi Yuli Kurniawati, Elsa Yuli Nur Azizah, Yuli Nur Z R Ridlo Zainur Rasyid Ridlo