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Rainbow Vertex Antimagic Coloring 2-Connection paada Keluarga Graf Tangga Ahmad Musyaffa' Hikamuddin; Dafik Dafik; Rafiantika Megahnia Prihandini
CGANT JOURNAL OF MATHEMATICS AND APPLICATIONS Vol 3, No 2 (2022): CGANT JOURNAL OF MATHEMATICS AND APPLICATIONS
Publisher : jcgant

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.25037/cgantjma.v3i2.88

Abstract

All graph in this paper are connected graph and simple graph. Let G = (V,E)be a connected graph. Rainbow vertex connection is the assignment of G that has interior vertices with different colors. The minimum number of colors from the rainbow vertex coloring in graph G is called rainbow vertex connection number. If wf(u) ̸= wf(v) for two different vertext u, v ∈ V (G) then f is called antimagic labeling for graph G. Rainbow vertex antimagic coloring is a combination between rainbow coloring and antimagic labeling. Graph G is called rainbow vertex antimagic coloring 2-connection if G has at least 2 rainbow paths from u − v. Rainbow vertex antimagic coloring 2-connection to denoted as rvac2(G). In this paper, we will study rainbow vertex antimagic coloring 2-connection on a family of graphs ladder that includes H-graph Hn for n ≥ 2, slide ladder graph SLn for n ≥ 2, and graph Octa-Chain OCn for n ≥ 2.
PEWARNAAN SISI r-DINAMIS PADA GRAF HASIL OPERASI AMALGAMASI TITIK KELUARGA GRAF POHON DAN KAITANNYA DENGAN KETERAMPILAN BERPIKIR TINGKAT TINGGI Lusia Dewi Minarti; Dafik Dafik; Susi Setiawani; Slamin Slamin; Arif Fatahillah
saintifika Vol 21 No 2 (2019)
Publisher : FKIP Universitas Jember

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (333.611 KB)

Abstract

Pewarnaan sisi dinamis suatu graf didefinisikan sebagai pemetaan dari ke himpunan warna sedemikian hingga memenuhi kondisi dan dimana adalah himpunan sisi yang bertetangga dengan dan adalah derajat titik . Nilai yang minimal sehingga graf memenuhi pewarnaan warna sisi dinamis disebut bilangan kromatik sisi dinamis, yang dinotasikan dengan Penelitian ini, peneliti menentukan bilangan kromatik pada graf hasil operasi amalgamasi titik dari keluarga graf pohon yaitu graf bintang dan graf sapu menggunakan metode deduktif aksiomatik. Hasil dari penelitian ini adalah teorema yang menyatakan bilangan kromatik pewarnaan sisi dinamis. Terdapat tiga teorema yang dihasilkan dari graf yang diteliti serta setiap tahap dalam penelitian ini dikaitkan dengan keterampilan berpikir tingkat tinggi.
PEWARNAAN TITIK TOTAL ANTIAJAIB LOKAL PADA GRAF HASIL OPERASI KORONA DAN KAITANNYA DENGAN KETERAMPILAN BERPIKIR TINGKAT TINGGI Safira Izza Ghafrina; Slamin Slamin; Dafik Dafik; Arif Fatahillah; Antonius Cahya Prihandoko
saintifika Vol 20 No 2 (2018)
Publisher : FKIP Universitas Jember

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (548.905 KB)

Abstract

Penelitian ini merupakan pengembangan dari paper berjudul “Local Antimagic Vertex Coloring of a Graph” oleh Arumugam et al. mengenai pewarnaan titik dengan pelabelan sisi pada graf khusus yang bertujuan untuk menentukan pewarnaan titik total antiajaib lokal pada graf hasil operasi korona. Penelitian juga akan menganalisis tentang keterkaitan antara pewarnaan titik total antiajaib lokal dengan pewarnaan titik antiajaib lokal pada graf hasil operasi korona ; Dan Menganalisis kaitan keterampilan berpikir tingkat tinggi dalam menentukan pewarnaan titik total antiajaib lokal pada graf hasil operasi korona yang diteliti menggunakan Taksonomi Bloom Revisi. Dalam penelitian ini digunakan instrumen validasi untuk mengetahui pencapaian tingkat keterampilan berpikir tinggi. Hasilnya, ditemukan teorema baru yang membuktikan bahwa bilangan kromatik antiajaib lokal oleh Arumugam lebih besar dibandingkan bilangan kromatik total antiajaib lokal . Dalam penelitian ini juga menghasilkan kaitan keterampilan berpikir tingkat tinggi dalam menentukan pewarnaan titik total antiajaib lokal pada graf hasil operasi korona yang diteliti.
Resolving Dominating Set pada Graf Bunga dan Graf Roda Nabilah Ayu Az-Zahra; Dafik Dafik; R M Prihandini
CGANT JOURNAL OF MATHEMATICS AND APPLICATIONS Vol 4, No 1 (2023): CGANT JOURNAL OF MATHEMATICS AND APPLICATIONS
Publisher : jcgant

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.25037/cgantjma.v4i1.89

Abstract

All graphs in this paper are simple and connected graph. Let V (G) and E(G) bevertex set and edge set. A map f : .V (G) −→ {0, 2, ..., 2kv} and f : E(G) −→ {1, 2, ..., ke} are sind to be an irregular reflexive labelling where k = max{2kv, ke} for kv, ke are natural number. The weight of edge u, v ∈ E(G) under f is w(u) = f(u)+Σuv∈V (G)f(uv). The function f is called local edge irregular reflexive labeling if every two adjacent edges has distinct weight and weight of a edge is defined as the sum of the labels of edge and the labels of all vertex incident this edgeWhen we assign each edge of G with a color of the edge weight w(uv), thus we say the graph G admits a local edge irregular reflexive coloring. The minimum number of colors produced from local edge irregular reflexive coloring of graph G is reflexive local irregular chromatic number denoted by χlrecs(G). Furthermore, the minimum k required such that χlrecs(G) = χ(G) is called a local reflexive edge color strength, denoted by lrecs(G). In this paper, we learn about the local edge irregular reflexive coloring and obtain lrecs(G) of planar related graphs.
Rainbow Connection pada Graf Siput, Graf Tunas Kelapa dan Graf Lotus Indi Izzah Makhfduloh; Dafik Dafik; R Adawiyah
CGANT JOURNAL OF MATHEMATICS AND APPLICATIONS Vol 4, No 1 (2023): CGANT JOURNAL OF MATHEMATICS AND APPLICATIONS
Publisher : jcgant

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.25037/cgantjma.v4i1.91

Abstract

Graph colouring is giving colour to a set of vertices and a set of edges on a graph. The condition for colouring a graph is that each colour is different for each neighbouring graph member. Graph colouring can be done by mapping a different colour to each vertex or edge. Rainbow colouring is part of the rainbow-connected edge colouring, where every graph G has a rainbow path. A rainbow path in graph G is formed if two vertices on graph G do not have the same colour. The minimum number of colours in a rainbow-connected graph is called the rainbow connection number denoted by rc(G). The graphs used in this study are the snail graph (Sn), the coconut shoot graph (CRn,m) and the lotus graph (Lon).
Strong Dominating Set pada Graf Helm Tertutup dan Graf Kincir Angin Belanda Imanul Umar Hawari; Dafik Dafik; Robiatul Adawiyah
CGANT JOURNAL OF MATHEMATICS AND APPLICATIONS Vol 4, No 1 (2023): CGANT JOURNAL OF MATHEMATICS AND APPLICATIONS
Publisher : jcgant

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.25037/cgantjma.v4i1.95

Abstract

A set D⊆ V(G) is a dominating set if every vertex of u ∈ V(G) satisfies one of the conditions u is an element of D or u is a neighbor of some point v ∈ D. The minimum cardinality of dominating set in graph G is called domination number which is symbolized by γ(G). Strong dominating set of a graph G is a subset of V(G) where the condition is that the dominating point must have the greatest degree or be equal to the dominating point. The minimum cardinality of strong dominating set is called strong domination number which is symbolized by γ_st(G). In this study, the graphs to be examined are the closed helmet graph (CH_n) with n≥ 3 and the dutch windmill graph (D_{n,5}) with n≥2.
On Irregular Colorings of Unicyclic Graph Family Arika Indah Kristiana; Dafik Dafik; Qurrotul A’yun; Robiatul Adawiyah; Ridho Alfarisi
CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 7, No 4 (2023): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI
Publisher : Mathematics Department, Universitas Islam Negeri Maulana Malik Ibrahim Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.18860/ca.v7i4.16917

Abstract

Irregular coloring is a proper coloring and each vertex on a graph must have a different code. The color code of a vertex v is  where  and    is the number of vertices that are adjacent to v and colored i. The minimum k-color used in irregular coloring is called the irregular chromatic number and denoted by . In this paper, we discuss the irregular chromatic number for the bull graph, pan graph, sun graph, peach graph, and caveman graph. 
Enhancing Students' Combinatorial Thinking for Graceful Coloring Problem: A STEM-Based, Research-Informed Approach in ATM Placement Robiatul Adawiyah; Arika Indah Kristiana; Dafik Dafik; Muhammad Lutfi Asy’ari; I Made Tirta; Zainur Rasyid Ridlo; Elsa Yuli Kurniawati
Tadris: Jurnal Keguruan dan Ilmu Tarbiyah Vol 8, No 1 (2023): Tadris: Jurnal Keguruan dan Ilmu Tarbiyah
Publisher : Universitas Islam Negeri Raden Intan Lampung

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.24042/tadris.v8i1.15176

Abstract

Combinatorial generalization thinking, a component of higher-order thinking skills, encompasses perception (pattern identification), expressions (pattern illustration), symbolic expressions (pattern formulation), and manipulation (combinatorial results application). Implementing a research-based learning (RBL) model with a Science, Technology, Engineering, and Mathematics (STEM) approach can effectively transform students' learning processes, promoting experiential learning through the integration of STEM elements. This study employs a mixed-method research design, combining quantitative and qualitative methodologies, to evaluate the impact of this RBL-STEM model on students' ability to solve graceful coloring problems, hence developing their combinatorial thinking skills. Two distinct classes, one experimental and one control, were analyzed for statistical homogeneity, normality, and independent t-test comparisons. Results indicated a significant post-test t-score difference between the two groups. Consequently, we conclude that the RBL model with a STEM approach significantly enhances students' combinatorial generalization thinking skills in solving graceful coloring problems. As this research provides empirical evidence of the effectiveness of a STEM-based RBL model, educators, and curriculum developers are encouraged to incorporate this approach into their instructional strategies for enhancing combinatorial thinking skills. Future research should consider various contexts and diverse student populations to further validate and generalize these findings.
Enhancing Students' Combinatorial Thinking for Graceful Coloring Problem: A STEM-Based, Research-Informed Approach in ATM Placement Robiatul Adawiyah; Arika Indah Kristiana; Dafik Dafik; Muhammad Lutfi Asy’ari; I Made Tirta; Zainur Rasyid Ridlo; Elsa Yuli Kurniawati
Tadris: Jurnal Keguruan dan Ilmu Tarbiyah Vol 8, No 1 (2023): Tadris: Jurnal Keguruan dan Ilmu Tarbiyah
Publisher : Universitas Islam Negeri Raden Intan Lampung

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.24042/tadris.v8i1.15176

Abstract

Combinatorial generalization thinking, a component of higher-order thinking skills, encompasses perception (pattern identification), expressions (pattern illustration), symbolic expressions (pattern formulation), and manipulation (combinatorial results application). Implementing a research-based learning (RBL) model with a Science, Technology, Engineering, and Mathematics (STEM) approach can effectively transform students' learning processes, promoting experiential learning through the integration of STEM elements. This study employs a mixed-method research design, combining quantitative and qualitative methodologies, to evaluate the impact of this RBL-STEM model on students' ability to solve graceful coloring problems, hence developing their combinatorial thinking skills. Two distinct classes, one experimental and one control, were analyzed for statistical homogeneity, normality, and independent t-test comparisons. Results indicated a significant post-test t-score difference between the two groups. Consequently, we conclude that the RBL model with a STEM approach significantly enhances students' combinatorial generalization thinking skills in solving graceful coloring problems. As this research provides empirical evidence of the effectiveness of a STEM-based RBL model, educators, and curriculum developers are encouraged to incorporate this approach into their instructional strategies for enhancing combinatorial thinking skills. Future research should consider various contexts and diverse student populations to further validate and generalize these findings.
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 QurrotaA’yuniArRuhimat A’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 Mar’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