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RAINBOW VERTEX CONNECTION NUMBER OF BULL GRAPH, NET GRAPH, TRIANGULAR LADDER GRAPH, AND COMPOSITION GRAPH (P_n [P_1 ]) Annadhifi, Muhammad Ilham Nurfaizi; Adawiyah, Robiatul; Dafik, Dafik; Suparta, I Nengah
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 18 No 3 (2024): BAREKENG: Journal of Mathematics and Its Application
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol18iss3pp1665-1672

Abstract

The rainbow connection was first introduced by Chartrand in 2006 and then in 2009 Krivelevich and Yuster first time introduced the rainbow vertex connection. Let graph be a connected graph. The rainbow vertex-connection is the assignment of color to the vertices of a graph , if every vertex on the graph is connected by a path graph that has interior vertices in different colors. The minimum number of colors from the rainbow vertex coloring in the graph is called rainbow vertex connection number which is denoted . The results of the research are the rainbow vertex connection number of bull graph, net graph, triangular ladder graph, and graph composition (Pn[P1]).
Development of Interactive Learning Media Based on Augmented Reality for Solid Geometry Concepts Lestari, Wahyu; Dafik, Dafik
JDIME: Journal of Development and Innovation in Mathematics Education Vol. 3 No. 1 (2025): Journal of Development and Innovation in Mathematics Education
Publisher : Insitut Agama Islam Negeri Kerinci

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.32939/jdime.v3i1.5060

Abstract

This study aims to develop an interactive learning medium based on Augmented Reality (AR) for teaching three-dimensional geometric shapes to junior high school students. The medium was designed to enhance students’ understanding of geometric concepts, particularly in terms of spatial visualization. The research employed a development approach using the ADDIE model (Analysis, Design, Development, Implementation, Evaluation). The development process involved validation by content and media experts, as well as trials conducted with students to evaluate their responses and the medium’s effectiveness. The results indicated that the developed AR learning medium was highly valid, with a material validity score of 94.5% and a media design validity score of 91.3%. Student response questionnaires revealed that 93.7% of students felt the medium helped them better understand the concepts of three-dimensional figures, while 89.1% stated that the medium made learning mathematics more engaging and enjoyable. Additionally, the average pretest score was 61.7, which increased to 84.2 in the posttest. A paired t-test showed a significance value of p < 0.01, indicating that the improvement in learning outcomes was statistically significant. The AR learning medium was thus proven to be valid and effective in assisting students in visualizing complex geometric objects, as well as making the learning process more engaging and interactive. Consequently, this study recommends the use of AR as an effective alternative learning tool to enhance students' mathematical understanding at the junior high school level.
On H-irregular reflexive labeling of graph Marsidi, Marsidi; Agustin, Ika Hesti; Dafik, Dafik; Rahman, Md. Saidur; Sullystiawati, Lusia Herni
CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 8, No 2 (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.v8i2.23753

Abstract

By an irregular reflexive  labeling, we mean a function  and  such that  if  and  if , where  max . Let , the irregular reflexive  labeling is called an -irregular reflexive -labeling of graph  if every two different sub graphs  and  isomorphic to , it holds , where . The minimum  for graph  which has an -irregular reflexive -labeling is called the reflexive  strength of graph and denoted by . In this paper we initiate to study the lower bound of the reflexive  strenght of graphs and the reflexive  strenght of flower, Shack  and book graph, where  isomorphic to and , respectively.
Optimizing Data Classification in Support Vector Machines Using Metaheuristic Algorithms Awalin, Qonita Ilmi; Agustin, Ika Hesti; Hadi, Alfian Futuhul; Dafik, Dafik; Sunder, R.
CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 9, No 2 (2024): 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.v9i2.29320

Abstract

To categorize patient diagnosis data related to Chronic Kidney Disease (CKD), this study compares the classification performance of Support Vector Machines (SVM) enhanced by Particle Swarm Optimization (PSO) and Genetic Algorithm (GA). CKD is a severe illness in which the kidneys fail to adequately filter blood and perform their normal functions. This study utilized secondary data consisting of patient conditions and health information. Based on references from CKD-related journals, 15 independent variables and one dependent variable were selected from an initial set of 54 variables. To address the issue of unbalanced data, an oversampling technique was applied, and the data was subsequently split into 80% for training and 20% for testing. During the training phase, SVM-PSO and SVM-GA models were developed, and the gamma value was optimized using the RBF kernel function of SVM. The results indicated that in classifying CKD patient diagnosis data, the SVM-PSO model (97.54% accuracy) outperformed the SVM-GA model (97.37% accuracy). This finding suggests that PSO-based hyperparameter optimization yields a superior model for data classification
Super (a, d)-hyperedge antimagic total labeling on hypergraphs of the volcano graph, semi parachute graph, and comb product graph Adawiyah, Robiatul; Asari, Okta Endri; Dafik, Dafik; Kristiana, Arika Indah; Prihandini, Rafiantika Megahnia; Rohini, A
Alifmatika (Jurnal pendidikan dan pembelajaran Matematika) Vol 7 No 2 (2025): Alifmatika - December
Publisher : Fakultas Tarbiyah Universitas Ibrahimy

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.35316/alifmatika.2025.v7i2.391-408

Abstract

In graph theory, understanding the labeling of graphs and hypergraphs provides valuable insights into their structural properties and applications. A hypergraph generalizes the notion of a conventional graph, defined as a mathematical structure built from a vertex set V and a hyperedge set E, where each hyperedge is allowed to connect two or more vertices simultaneously. The essential distinction between a graph and a hypergraph lies in their edges. While in a graph a single edge connects exactly two vertices, in a hypergraph a single hyperedge may connect any number of vertices, including two. A hypergraph is considered to admit a super (a, d) -hyperedge antimagic total labeling, such that the vertex label functions f: V(H)  1, 2, 3, ....., V(H) then f: E(H)  V(H) + 1, ....., V(H) + V(H) and weight w(ei) = ∑ f(ei) + ∑ f(Vi,j), where i denotes the number of hyperedges, j represents the number of vertices contained in a hyperedge, and e_i refers to the set of vertices and its associated edges with weight w(ei) for each hyperedge. A super (a, d) -hyperedge antimagic total labeling is formulated as a labeling scheme based on arithmetic progressions, where ???? serves as the initial value and d denotes the common difference between consecutive labels. In this scheme, the total weight of a hyperedge is determined by deriving from the sum of the vertex labels and the label of the respective hyperedge. The labels are arranged in an arithmetic sequence, ensuring that each hyperedge has a distinct weight. This study focuses on several special classes of hypergraphs, namely, the volcano graph, the semi-parachute graph, and the comb product of graphs, to implement and examine the characteristics of the super (a, d)-hyperedge antimagic total labeling. By focusing on these graph classes, the study contributes to combinatorics by offering a deeper understanding of hypergraph labeling schemes and their potential applications in network theory, coding theory, and data modeling.
On Local Antimagic b-Coloring and Its Application for STGNN Time Series Forecasting on Horizontal Farming R. Sunder; Ika Hesti Agustin; Dafik Dafik; Ika Nur Maylisa; N. Mohanapriya; Marsidi Marsidi
CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 10, No 1 (2025): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI
Publisher : Mathematics Department, Maulana Malik Ibrahim State Islamic University of Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.18860/cauchy.v10i1.29968

Abstract

This article discusses a local antimagic coloring which is a combination between antimagic labeling and coloring. It is a new notion. We define a vertex weight of  as  where  is the set of edges incident to . The bijection  is said to be a local antimagic labeling if for any two adjacent vertices, their vertex weights must be distinct. Furthermore  a coloring of a graph is a proper coloring of the vertices of  such that in each color class there exists a vertex having neighbors in all other  color classes. If we assign color on each vertex by the vertex weight  such that it induces a graph coloring satisfying coloring property, then this concept falls into a local antimagic coloring of graph. A local antimagic chromatic number, denoted by , is the maximum number of colors chosen for any colorings generated by local antimagic coloring of . In this paper we initiate to explore some new lemmas or theorems regarding to . Furthermore, to see the robust application of local antimagic coloring, at the end of this paper we will analyse the implementation of local antimagic coloring on Graph Neural Networks (GNN) multi-step time series forecasting on for NPK (Nitrogen, Phosphorus, and Potassium) concentration of companion plantations.
Students' Climate Change Literacy: Implementing RBL-STEM Makerspace Materials on Recycling Plastic Waste into Ecobricks Tri Dyah Prastiti; Idha Novianti; Endang Wahyuningrum; Dafik Dafik; Zainur Rasyid Ridlo; Indah Lutfiatul Mursyidah; Okti Anis Safiati
Prisma Sains : Jurnal Pengkajian Ilmu dan Pembelajaran Matematika dan IPA IKIP Mataram Vol. 14 No. 2: April 2026
Publisher : Universitas Pendidikan Mandalika

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.33394/j-ps.v14i2.20074

Abstract

Climate change is an increasingly significant concern due to rising sea levels and extreme weather events. This phenomenon has made specific regions uninhabitable or unsuitable for agriculture. In addition, promoting climate change literacy is one of the key factors in addressing the posed challenges. Therefore, this research aimed to analyze the implementation of Research-Based Learning with Science, Technology, Engineering, and Mathematics (RBL-STEM) materials to promote students' climate change literacy, using a mixed-methods design. This research employed a mixed-methods design. Quantitative methods were used to analyze climate change literacy, while qualitative methods examined learning activities and phase portraits under the implementation of the materials. The two classes used comprised a control class of 40 students and an experimental class of 42 students. Meanwhile, the instruments used were interviews, questionnaires, and students’ climate change literacy tests. The results showed that there were differences between the control and experimental classes using an independent sample t-test with a sig value (2-tailed) of 0.0048 (<0.05). In the context of this research, the implementation of the materials promoted students’ climate change literacy in recycling plastic waste into ecobricks.
Locating Metric Coloring on The Cherry Blossom, Sun Flower and Closed Dutch Windmill Graphs Arika Indah Kristiana; Agustina Hotimatus Khusnul; Dafik Dafik
CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 10, No 2 (2025): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI
Publisher : Mathematics Department, Maulana Malik Ibrahim State Islamic University of Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.18860/cauchy.v10i2.33636

Abstract

Locating metric coloring is a variation of metric coloring in graphs that integrates vertex coloring with the uniqueness of metric representations. In this coloring, each vertex in a connected graph  is assigned a color such that the distance vectors to each color class are distinct for every pair of different vertices. Let  be a coloring function (not necessarily proper). The coloring ccc is called a locating metric coloring if, for any two distinct vertices , their distance vectors , so it is obtained represents the partition of vertices by color classes. Thus, for every vertex, the distance vector  are different. Vertices may share the same color, whether adjacent or not, as long as their metric representations are unique. The smallest number of colors required for such a coloring is called the locating metric chromatic number, denoted  T This study focuses on analyzing locating metric coloring for three specific graphs: the Cherry Blossom graph , the Sun Flower graph , and the Closed Dutch Windmill graph . These graphs were chosen due to the absence of prior research on their locating metric coloring properties. The research method combines pattern recognition and a deductive-axiomatic approach. The proof process begins by determining lower bounds, followed by the construction of upper bounds through coloring function analysis. The resulting locating metric chromatic numbers for each graph are then established.
Analysis of Resolving Efficient Dominating Set and Its Application Scheme in Multi-Step Time Series Forecasting of pH and Soil Moisture in Horizontal Farming Kamal Dliou; Adinda Putri Aziza; Dafik Dafik; Arika Indah Kristiana; Dwi Agustin Retnowardani
CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 10, No 1 (2025): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI
Publisher : Mathematics Department, Maulana Malik Ibrahim State Islamic University of Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.18860/cauchy.v10i1.29960

Abstract

This research focuses on the analyzing the Resolving Efficient Dominating Set (REDS) and its application scheme in horizontal farming using the Spatial Temporal Graph Neural Network (STGNN). Soil moisture and pH are crucial factors that affect the growth and yield, as they directly impact productivity and plant health. In cases where soil moisture and pH are lacking, various types of companion planting need to be watered. In such planting systems, a central role is needed to monitor soil moisture and pH levels effectively. The placement of operators in this system requires the application of mathematical concepts, specifically graph theory. In this study, we explore graph theory, particularly the Resolving Efficient Dominating Set. This involves ensuring that each vertex  is dominated by exactly one vertex in D, with no adjacent with another vertex, and the representation of vertex  concerning  is not the same. To effectively address this issue, including soil moisture and pH data, is required to predict future soil moisture and pH values in companion farming. Spatial Temporal Graph Neural Network (STGNN) technique proves to be useful in solving the problem of soil moisture and pH by understanding and modeling multi-step time series data. This technique aids in effectively managing and optimizing horizontal farming.
Theoretical study of the II-VI solar cells semiconductor material arrangements effect using the one-dimensional Schrodinger equation Tamara Pingki; Dafik Dafik; Bambang Supriadi
Journal of Physics: Theories and Applications Vol 8, No 2 (2024): Journal of Physics: Theories and Applications
Publisher : Universitas Sebelas Maret

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.20961/jphystheor-appl.v8i2.82285

Abstract

Solar cells are electronic devices that function to convert light energy from sun into electrical energy. Solar cells can work well if the materials used are also right so they can absorb light energy to the maximum. The solar cell materials used in this study are II-VI semiconductors, there are CdS (P), CdSe (Q), and CdTe (R). The purpose of this study was to find the combination of materials has the largest transmission coefficient which was analyzed using the Schrodinger equation (analytic) and Matlab R2022a (numeric). The greater the transmission coefficient, the greater the light energy absorbed by the solar cells, so that the generated electrical energy is also greater. The materials are arranged into 3 uniform arrangements and 6 combined arrangements with a maximum electron energy of 1 eV. The results showed that the largest transmission coefficient in the CdS array was 0.9925 at 1.0000 eV, the largest transmission coefficient in the CdSe array was 1.0000 at 0.8140 eV, and the largest transmission coefficient in the CdTe array was 1.0000 at 0.7330 eV. Meanwhile, in the combined arrangement, the biggest transmission value is 0.9823 at 0.9570 eV in the QPR and RPQ arrangements.
Co-Authors A Arynda A H Rahmatillah A. Y. Harsya Adawiyah, R Adelia Putri Liowardani Adinda Putri Aziza Agnes Ika Nurvitaningrum, Agnes Ika Agrita Kanty Purnapraja, Agrita Kanty Agustina Hotimatus Khusnul Agustina M. Agustina Muharromah, Agustina Ahmad Adi Ahmad Musyaffa&#039; 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 A’yun, Qurrotul Bambang Supriadi 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 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&#039;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 Ida Ariska Idha Novianti Ika Hesti A. Ika Hesti Agustin, Ika Hesti Ika Mareta Ika Nur Maylisa Imanul Umar Hawari Imro’atun Rofikah Indah Lutfiatul Mursyidah 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 Kamal Dliou Karinda Rizqy Aprilia, Karinda Rizqy Khilyah Munawaroh Kholifatu Rosyidah Kholifatur Rosyidah 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 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 N. Mohanapriya 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 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 R. Sunder 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 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 Tamara Pingki 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