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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

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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. 
The Distance Irregular Reflexive k-Labeling of Graphs Agustin, Ika Hesti; Dafik, Dafik; Mohanapriya, N.; Marsidi, Marsidi; Cangul, Ismail Naci
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.v7i4.19747

Abstract

A total k-labeling is a function fe from the edge set to the set {1, 2, . . . , ke} and a function fv from the vertex set to the set {0, 2, 4, . . . , 2kv}, where k = max{ke, 2kv}. A distance irregular reflexive k-labeling of the graph G is the total k-labeling, if for every two different vertices u and u 0 of G, w(u) 6= w(u 0 ), where w(u) = Σui∈N(u)fv(ui) + Σuv∈E(G)fe(uv). The minimum k for graph G which has a distance irregular reflexive k-labelling is called distance reflexive strength of the graph G, denoted by Dref (G). In this paper, we determine the exact value of distance reflexive strength of some connected graphs, namely path, star, and friendship graph.
On the study of Rainbow Antimagic Coloring of Special Graphs Dafik, Dafik; Wahidah, Riniatul Nur; Albirri, Ermita Rizki; Husain, Sharifah Kartini Said
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.v7i4.17836

Abstract

Let  be a connected graph with vertex set  and edge set . The bijective function  is said to be a labeling of graph where  is the associated weight for edge . If every edge has different weight, the function  is called an edge antimagic vertex labeling. A path  in the vertex-labeled graph , with every two edges  satisfies  is said to be a rainbow path. The function  is called a rainbow antimagic labeling of , if for every two vertices , there exists a rainbow  path. Graph  admits the rainbow antimagic coloring, if we assign each edge  with the color of the edge weight  . The smallest number of colors induced from all edge weights of edge antimagic vertex labeling is called a rainbow antimagic connection number of , denoted by . In this paper, we study rainbow antimagic connection numbers of octopus graph , sandat graph , sun flower graph , volcano graph  and semi jahangir graph Jn.
On Rainbow Antimagic Coloring of Joint Product of Graphs Septory, Brian Juned; Susilowati, Liliek; Dafik, Dafik; Venkatachalam, M.
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.v7i4.17471

Abstract

Let  be a connected graph with vertex set  and edge set . A bijection  from  to the set  is a labeling of graph . The bijection  is called rainbow antimagic vertex labeling if for any two edge  and  in path , where  and . Rainbow antimagic coloring is a graph  which has a rainbow antimagic labeling. Thus, every rainbow antimagic labeling induces a rainbow coloring G where the edge weight  is the color of the edge . The rainbow antimagic connection number of graph  is the smallest number of colors of all rainbow antimagic colorings of graph , denoted by . In this study, we studied rainbow antimagic coloring and have an exact value of rainbow antimagic connection number of joint product of graph  where  is graph , graph , graph , graph  and graph .
On Irregular Colorings of Unicyclic Graph Family Kristiana, Arika Indah; Dafik, Dafik; A’yun, Qurrotul; Adawiyah, Robiatul; Alfarisi, Ridho
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. 
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