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On The Metric Dimension with Non-isolated Resolving Number of Some Exponential Graph S. M. Yunika; Slamin Slamin; Dafik Dafik; Kusbudiono Kusbudiono
UNEJ e-Proceeding 2016: Proceeding The 1st International Basic Science Conference
Publisher : UPT Penerbitan Universitas Jember

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Abstract

Let w, w ∈ G = (V, E). A distance in a simple, undirected and connected graph G, denoted by d(v, w), is the length of the shortest path between v and w in G. For an ordered set W = {w1, w2, w3, . . . , wk} of vertices and a vertex v ∈ G, the ordered k-vector r(v|W) = (d(v, w1), d(v, w2), . . . , d(v, wk)) is representations of v with respect to W. The set W is called a resolving set for G if distinct vertices of G have distinct representations with respect to W. The metric dimension dim(G) of G is the minimum cardinality of resolving set for G. The resolving set W of graph G is called non-isolated resolving set if subgraph W is induced by non-isolated vertex. While the minimum cardinality of non-isolated resolving set in graph is called a non-isolated resolving number, denoted by nr(G). In this paper we study a metric dimension with non-isolated resolving number of some exponential graph.
On Total r-Dynamic Coloring of Several Classes of Graphs and Their Related Operations Kusbudiono Kusbudiono; Desi Febriani Putri; Dafik Dafik; Arika Indah Kristiana
UNEJ e-Proceeding 2016: Proceeding The 1st International Basic Science Conference
Publisher : UPT Penerbitan Universitas Jember

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Abstract

All graphs in this paper are simple, connected and undirected. Let r, k be natural numbers. By a proper k-coloring of a graph G, we mean a map c : V (G) → S, where |S| = k, such that any two adjacent vertices receive different colors. A total r-dynamic coloring is a proper k-coloring c of G, such that ∀v ∈ V (G), |c(N(v))| ≥ min[r, d(v) + |N(v)|] and ∀uv ∈ E(G), |c(N(uv))| ≥ min[r, d(u) + d(v)]. The total r-dynamic chromatic number, written as χ ′′r (G), is the minimum k such that G has an r-dynamic k-coloring. Finding the total r-dynamic chromatic number is considered to be a NP-Hard problems for any graph. Thus, in this paper, we initiate to study χ′′ r (G) of several classes of graphs and and their related operations.
The Rainbow (1,2)-Connection Number of Exponential Graph and It’s Lower Bound Gembong A. W.; Dafik Dafik; Ika Hesti Agustin; Slamin Slamin
UNEJ e-Proceeding 2016: Proceeding The 1st International Basic Science Conference
Publisher : UPT Penerbitan Universitas Jember

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Abstract

Let G = (V, E) be a simple, nontrivial, finite, connected and undirected graph. Let c be a coloring c : E(G) → {1, 2, . . . , k}, k ∈ N. A path in an edge colored graph is said to be a rainbow path if no two edges on the path have the same color. An edge colored graph G is rainbow connected if there exists a rainbow u − v path for every two vertices u and v of G. The rainbow connection number of a graph G, denoted by rc(G), is the smallest number of k colors required to edge color the graph such that the graph is rainbow connected. Furthermore, for an l-connected graph G and an integer k with 1 ≤ k ≤ l, the rainbow k-connection number rck(G) of G is defined to be the minimum number of colors required to color the edges of G such that every two distinct vertices of G are connected by at least k internally disjoint rainbow paths. In this paper, we determine the exact values of rainbow connection number of exponential graphs, namely Path of ladder as exponent, Cycle of Ladder as exponent, Cycle of Triangular Ladder as exponent, Cycle of Complete as exponent. We also proved that rc2(G) = diam(G) + 1.
The Analysis of r-dynamic Vertex Colouring on Graph Operation Of Shackle Novita Sana Susanti; Dafik Dafik
UNEJ e-Proceeding 2016: Proceeding The 1st International Basic Science Conference
Publisher : UPT Penerbitan Universitas Jember

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Abstract

Let G be a simple, connected and undirected graph and r, k be natural numbers. An edge coloring that uses k colors is a k-edge coloring. Thus a graph G can be described as a function c : V (G) → S, where |S| = k, such that any two adjacent vertices receive different colors. 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. In this paper, we will study the existence of r-dynamic k-coloring when G is shackle of wheel graph. As we know, that a shackle operation of H denoted by shack(H, v, n) is a shackle with vertex as the connector. We also can generated shackle graph with edge connector or subgraph as the connector.
Construction of Super H-Antimagicness of Graph by Uses a Partition Technique with Cancelation Number Rafiantika Megahnia Prihandini; Dafik Dafik; Ika Hesti Agustin
UNEJ e-Proceeding 2016: Proceeding The 1st International Basic Science Conference
Publisher : UPT Penerbitan Universitas Jember

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Abstract

Abstract—The graph operation is one method to construct a new graph by applying the operation to two or more graph. One of graph operation is amalgamation, let {Hi} be a finite collection of nontrivial, simple and undirected graphs and let each Hi has a fixed vertex vj called a terminal. The terminal of graph operation is formed by taking all the Hi’s and identifying their terminal. When Hi are all isomorphic graphs, for any positif integer n, we denote such amalgamation by G = Amal(H, v, n), where n denotes the number of copies of H and v is the terminal. The graph G is said to be an (a, d)-H-antimagic total graph if there exist a bijective function f : V (G) ∪ E(G) → {1, 2, . . . , |V (G)| + |E(G)|} such that for all subgraphs isomorphic to H, the total H-weights W(H) = ∑v∈V (H) f(v) + ∑e∈E(H) f(e) form an arithmetic sequence {a, a + d, a + 2d, ..., a + (n − 1)d}, where a and d are positive integers and n 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 connected of graph G = Amal(H, Ps+2, n) by uses a partition technique with cancelation number. The result is graph G = Amal(H, Ps+2, n) admits a super(a, d)-H antimagic total labeling for almost feasible difference d.
On the Rainbow Vertex Connection Number of Edge Comb of Some Graph Agustina M.; Dafik Dafik; Slamin Slamin; Kusbudiono Kusbudiono
UNEJ e-Proceeding 2016: Proceeding The 1st International Basic Science Conference
Publisher : UPT Penerbitan Universitas Jember

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Abstract

By an edge comb, we mean a graph formed by combining two graphs G and H, where each edge of graph G is replaced by the which one edge of graph H, denote by G D H. A vertex colored graph G D H = (V (G D H);E(G D H)) is said rainbow vertex-connected, if for every two vertices u and v in V (G D H), there is a u ???? v path with all internal vertices have distinct color. The rainbow vertex connection number of G D H, denoted by rvc(G D H) is the smallest number of color needed in order to make G D H rainbow vertex-connected. This research aims to find an exact value of the rainbow vertex connection number of exponential graph, namely rvc(G D H) when G D H are Pn D Btm, Sn D Btm, Ln D Btm, Fm;n D Btp, rvc(Pn D Sm), rvc(Cn D Sm), and rvc(Wn D Sm) Wn D Btm. The result shows that the resulting rainbow vertex connection attain the given lower bound.
On The Total r-dynamic Coloring of Edge Comb Product graph G D H Dwi Agustin Retno Wardani; Dafik Dafik; Antonius C. Prihandoko; Arika I. Kristiana
UNEJ e-Proceeding 2016: Proceeding The 1st International Basic Science Conference
Publisher : UPT Penerbitan Universitas Jember

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Abstract

Given that two natural numbers r, k. By a proper total k-coloring of a graph G, we mean a map c : V (G) ∪ E(G) → {1, 2, . . . , k}, such that any two adjacent vertices and incident edges receive different colors. A total r-dynamic coloring is a proper k-coloring c of G, such that ∀v ∈ V (G), |c(N(v))| ≥ min{r, d(v) + |N(v)|} and ∀e ∈ E(G), |c(N(e))| ≥ min{r, d(v) + d(u)}. The total r-dynamic chromatic number, written as χ ”r(G), is the minimum k such that G has an r-dynamic total k-coloring. A total r-dynamic coloring is a natural extension of r-dynamic coloring in which we consider more condition of the concept, namely not only assign a color on the vertices as well as on the edges. Consequently, this study will be harder. In this paper, we will initiate to analyze a total r-dynamic of an edge comb product of two graphs, denoted by H D K, where H is path graph and K is any special graph. The result shows that the total r-dynamic chromatic number of Pn D K.
Super (a, d)-Edge Antimagic Total Labeling of Connected Ferris Wheel Graph Djoni Budi Sumarno; D Dafik; Kiswara Agung Santoso
Jurnal ILMU DASAR Vol 15 No 2 (2014)
Publisher : Fakultas Matematika dan Ilmu Pengetahuan Alam Universitas Jember

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (127.85 KB) | DOI: 10.19184/jid.v15i2.1051

Abstract

Let G be a simple graph of order p and size q. Graph G is called an (a,d)-edge-antimagic totalifthereexistabijectionf :V(G)∪E(G)→{1,2,...,p+q}suchthattheedge-weights,w(uv)= f(u)+f(v)+f(uv); u, v ∈ V (G), uv ∈ E(G), form an arithmetic sequence with first term a and common difference d. Such a graph G is called super if the smallest possible labels appear on the vertices. In this paper we study super (a, d)-edge antimagic total properties of connected of Ferris Wheel F Wm,n by using deductive axiomatic method. The results of this research are a lemma or theorem. The new theorems show that a connected ferris wheel graphs admit a super (a, d)-edge antimagic total labeling for d = 0, 1, 2. It can be concluded that the result of this research has covered all feasible d. Key Words : (a, d)-edge antimagic vertex labeling, super (a, d)-edge antimagic total labeling, Ferris Wheel graph FWm,n.  
THE LEVEL OF CRITICAL THINKING SKILL ON SOLVING TWO-DIMENSIONAL ARITHMETICS PROBLEMS THROUGH RESEARCH-BASED LEARNING Suntusia Suntusia; Dafik Dafik; Hobri Hobri
Alifmatika (Jurnal pendidikan dan pembelajaran Matematika) Vol 3 No 1 (2021): Alifmatika - June
Publisher : Fakultas Tarbiyah Universitas Ibrahimy

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (879.13 KB) | DOI: 10.35316/alifmatika.2021.v3i1.55-69

Abstract

Developing critical and collaborative thinking skills among learners was of significant importance in the 21st-century era. In this study, the researcher applied teaching and learning based on Research-Based Learning (RBL) to know the level of students critical thinking skill. The number of research samples was 30 students. This study used a triangulation research method, namely a combination of qualitative and quantitative methods. The quantitative method was obtained by using a learning outcome test and the qualitative method is obtained using a questionnaire and interview. Then the data that has been collected was analyzed using a t-test. Four students were chosen to represent critical thinking level 4, 13 students were chosen to represent Critical Thinking level 3, and 6 students were chosen to represent critical thinking level 2, 4 students were chosen to represent critical thinking level 1, and 3 students were chosen to represent critical thinking level 0. More subjects would be involved until the data was saturated. Students on low critical thinking were at Level 0. Based on the interpretation result of the t-test value, there was a significant difference between the control class and the experimental class, proved by the 0.000 figure in the statistical analysis. Therefore, it proved a significant difference in learning outcomes. However, the data that we obtained present a significant difference between the control class and the experimental class below 0.05. After we interpreted t-tabel = 2.04 on degrees of freedom 0.025, t-count of 0.000 was evident. Thus, a hypothesis was accepted since it was below 0.025. Qualitative methods show the results of interviews with 2 students.
Pengembangan Media Pembelajaran Adobe Animate Berbantuan Schoology Pada Materi Barisan dan Deret Aritmetika Desak Made Dwika Saniriati; Dafik Dafik; Randi Pratama Murtikusuma
Jurnal Riset Pendidikan dan Inovasi Pembelajaran Matematika (JRPIPM) Vol. 4 No. 2 (2021): JRPIPM APRIL 2021 VOLUME 4 NOMOR 2
Publisher : Universitas Negeri Surabaya

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.26740/jrpipm.v4n2.p132-145

Abstract

Penelitian ini bertujuan untuk mendeskripsikan proses dan hasil pengembangan media pembelajaran Adobe Animate berbantuan Schoology pada materi barisan dan deret aritmetika. Penelitian ini merupakan penelitian pengembangan dengan menggunakan model pengembangan Thiagarajan yang meliputi tahap definisi, tahap perancangan, tahap pengembangan, dan tahap penyebaran. Subjek penelitian ini adalah 20 siswa kelas XI dari salah satu sekolah menengah atas di Jember. Hasil penelitian menunjukkan tingkat kevalidan media pembelajaran ini berdasarkan penilaian validator memenuhi kategori œSangat Tinggi, tingkat kepraktisan berdasarkan angket respon pengguna memenuhi kategori œBaik, dan tingkat keefektifan menunjukkan 17 dari 20 siswa memperoleh nilai tes di atas KKM. Dengan demikian media pembelajaran Adobe Animate berbantuan Schoology pada materi barisan dan deret aritmetika dapat digunakan dalam proses pembelajaran karena telah memenuhi kriteria valid, praktis dan efektif.
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 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 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