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Veerebradiah Lokesha Reciprocal Status Index pada Komplemen Graf Total Diperumum dari Ring Bilangan Bulat Modulo Armeyntan, Tata Sutrafia; Turmudi, Turmudi; Jauhari, Mohammad Nafie
Jurnal Riset Mahasiswa Matematika Vol 3, No 4 (2024): Jurnal Riset Mahasiswa Matematika
Publisher : Mathematics Department, Maulana Malik Ibrahim State Islamic University of Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.18860/jrmm.v3i4.26657

Suppose R is a commutative ring and H is a subset of R. The complement of the generalized total graph is a simple graph with all the elements in R as points and two different points x and y are directly connected if and only if x and y are not elements of H. This study aims to determine the general form of the VLRS index in the generalized total graph complement of the integer ring modulo 2p where p greater than or equal to 3 is the prime number for H the set of zero divisors and H the set of units of the ring integer modulo 2p. The steps in this study are to determine the set of zero divisors and the set of units of the integer ring modulo 2p, determine the distance of each point in the complement of the generalized total graph of the ring of integers modulo 2p, determine the reciprocal state in the complement of the generalized total graph of the ring integer modulo 2p, and determine the VLRS index in the complement of the generalized total graph from the integer ring modulo 2p. The results of this study are related to the general form of the VLRS index on the complement of the generalized total graph of the 2p modulo integer ring where p is a prime number and p is greater than or equal to 3 with H the set of zero divisors and H the set of units of the 2p modulo integer ring.

Implementasi Algoritma Floyd Warshall dalam Pencarian Rute Terpendek Lokasi Tower Base Transceiver Station (BTS) pada PT Citra Akses Indonusa Savitri, Bella Nafa; Jauhari, Mohammad Nafie; Alisah, Evawati; Fahmi, Hisyam
Jurnal Riset Mahasiswa Matematika Vol 2, No 4 (2023): Jurnal Riset Mahasiswa Matematika
Publisher : Mathematics Department, Maulana Malik Ibrahim State Islamic University of Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.18860/jrmm.v2i4.16811

PT Citra Akes Indonusa is a company that operates on the expertise of information technology services in Banten Province. One of the services provided by the company requires the construction of a Base Transceiver Station (BTS) tower. The tower requires maintenance if there is damage to the network signal. As a result, the shortest route is needed to make it easier for employees to reach the tower location to be more effective. There are eight BTS tower locations in Tangerang Regency and three BTS tower locations in Tangerang City. The process of finding the shortest route in this study uses the Floyd Warshall algorithm, which is unique in finding the shortest route by comparing each edge of all edges that are passed. The process of testing the shortest route is done by selecting the starting point, then selecting several BTS tower locations. Next, the shortest route will be searched using the Floyd Warshall algorithm from each point of destination for the BTS tower location, then the BTS tower location will be selected first and so on until the last destination. The effectiveness of this shortest route search involves a comparison of the routes presented by Google Maps. Based on the results of 30 randomized trials on BTS tower locations, the average shortest route effectiveness was 25.54% compared to the route generated by Google Maps. This is due to the selection at each BTS tower destination location so as to make the route more effective.

On the Forgotten Index and Jacobson Graphs Associated with Integer Rings Modulo n Jauhari, Mohammad Nafie; Jannah, Shahnaz Latifatul; Turmudi, Turmudi; Nisfulaila, Intan
KUBIK Vol 9, No 2 (2024): KUBIK: Jurnal Publikasi Ilmiah Matematika
Publisher : Jurusan Matematika, Fakultas Sains dan Teknologi, UIN Sunan Gunung Djati Bandung

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.15575/kubik.v9i2.39585

This paper investigates the connections between the Jacobson graph and the algebraic properties of rings through the analysis of the Jacobson graph of the ring \mathbb{Z}_{3p}, where p is a prime number greater than 3. The Jacobson graph of a commutative ring R is constructed by taking the elements of R, excluding its Jacobson Radical, as vertices, and connecting two distinct vertices if 1 minus their product is not a unit in R. The F-Index is utilized to capture and represent the structural properties of the ring through its associated graph. A detailed examination of the Jacobson Radical, maximal ideals, and vertex degrees in \mathbb{Z}_{3p} leads to the calculation of the F-Index, providing insights into the graph’s connectivity and underlying algebraic structure. This study contributes to the intersection of algebra and graph theory, offering a foundation for further research into more complex algebraic structures.

Efektivitas E-Learning terhadap Kemampuan Koneksi Matematis Siswa di Kelompok Kerja Madrasah Tsanawiyah Kabupaten Tulungagung Elly Susanti; Turmudi Turmudi; Muhammad Nafie Jauhari; Sri Harini; Ahmad Lubab; Anisatur Rizqiyah
Jurnal Tadris Matematika Vol. 3 No. 1 (2020)
Publisher : Universitas Islam Negeri Sayyid Ali Rahmatullah Tulungagung

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.21274/jtm.2020.3.1.13-20

Madrasah students' mathematical connection skills need to be of particular concern in the process of learning mathematics. Connection skills are the base for students to connect concepts in mathematics, mathematical concepts with other science concepts and mathematical concepts with everyday life. One of the efforts made in overcoming this problem is to use e-learning. Descriptive quantitative research methods are used to see how effective e-learning is for students' mathematical connection abilities. A total of 30 students were selected as research samples for data collection. Data processing techniques were divided into control groups and subsequent experiments were analyzed using descriptive statistics. The results showed that the effectiveness of technology-based e-learning included moderate criteria with an ING score of 0.56, whereas the study group without e-learning included moderate criteria with an ING value of 0.29. In conclusion, there is an increase in student learning outcomes after using e-learning media. t-test was obtained > with 0.007 <∝ (0.05) indicating that e-learning was effective to improve the mathematical connection ability of Madrasah Tsanawiyah students.

On the Forgotten Index and Jacobson Graphs Associated with Integer Rings Modulo n Jauhari, Mohammad Nafie; Jannah, Shahnaz Latifatul; Turmudi, Turmudi; Nisfulaila, Intan
KUBIK Vol 9, No 2 (2024): KUBIK: Jurnal Publikasi Ilmiah Matematika
Publisher : Jurusan Matematika, Fakultas Sains dan Teknologi, UIN Sunan Gunung Djati Bandung

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.15575/kubik.v9i2.39585

This paper investigates the connections between the Jacobson graph and the algebraic properties of rings through the analysis of the Jacobson graph of the ring \mathbb{Z}_{3p}, where p is a prime number greater than 3. The Jacobson graph of a commutative ring R is constructed by taking the elements of R, excluding its Jacobson Radical, as vertices, and connecting two distinct vertices if 1 minus their product is not a unit in R. The F-Index is utilized to capture and represent the structural properties of the ring through its associated graph. A detailed examination of the Jacobson Radical, maximal ideals, and vertex degrees in \mathbb{Z}_{3p} leads to the calculation of the F-Index, providing insights into the graph’s connectivity and underlying algebraic structure. This study contributes to the intersection of algebra and graph theory, offering a foundation for further research into more complex algebraic structures.

Efektivitas Parameter Algoritma Cheapest Insertion Heuristic (CIH) dalam Menentukan Rute Terpendek Bus Sekolah Gratis Kota Malang Dayanti, Vivi; Jauhari, Mohammad Nafie
Jurnal Riset Mahasiswa Matematika Vol 4, No 1 (2024): Jurnal Riset Mahasiswa Matematika
Publisher : Mathematics Department, Maulana Malik Ibrahim State Islamic University of Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.18860/jrmm.v4i1.28244

This research focuses on changing parameters related to the initial value to optimize routes using the Cheapest Insertion Heuristic (CIH) algorithm, with the aim of achieving a more efficient or optimal solution. This research is a quantitative study that uses distance data between school locations from the official sources of the Department of Transportation and the Malang City government to measure the effectiveness of the CIH algorithm in determining the shortest route for school buses. This research begins by selecting two starting points using the CIH algorithm to find the optimal route. All possible pairs of starting points will be tried, then the correlation between the length of the shortest route generated and the factors considered, such as distance between the two starting points, eccentricity, betweenness centrality, eigenvector centrality, and closeness centrality, will be identified. The results showed that eigenvector centrality showed the strongest correlation with the shortest route length, with a Pearson correlation coefficient of 0,122.

Modifikasi Algoritma Floyd-Warshall Dalam Menemukan Rute Terpendek Pemadam Kebakaran Di Banyuwangi Salsabila, Wardatun Naura; Jauhari, Mohammad Nafie
Jurnal Riset Mahasiswa Matematika Vol 4, No 1 (2024): Jurnal Riset Mahasiswa Matematika
Publisher : Mathematics Department, Maulana Malik Ibrahim State Islamic University of Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.18860/jrmm.v4i1.30009

The research discusses finding fire truck routes on a graph that requires the shortest travel distance from the starting location to the final fire incident location. The objective of this research is to disiminate the application of a modified Floyd-Warshall Algorithm on a graph to find the shortest route for fire trucks. The method used in this study is the Floyd-Warshall Algorithm, which takes the minimum distance from one point to another on the graph and applies a dynamic algorithm, allowing it to correctly select the shortest route. The research results show that testing with the Floyd-Warshall Algorithm produced travel distances with an average effectiveness rate of 3.45%. This percentage indicates that the Floyd-Warshall Algorithm is effective, as it shows a shorter distance. Based on the research findings, it can be concluded that the modified Floyd-Warshall Algorithm applied to the graph can effectively find the shortest route based on the distance between fire stations and incident locations in Banyuwangi, as well as provides information on which routes can be taken based on shorter paths.

Pelatihan Penyusunan Bahan Ajar Berbasis Multimedia Bagi Guru-Guru Yayasan Ali Imron Pakamban Sumenep Jauhari, Mohammad Nafie; Juhari, Juhari; Jamhuri, Mohammad
JRCE (Journal of Research on Community Engagement) Vol 2, No 1 (2020): Journal of Research on Community Engagement
Publisher : Universitas Islam Negeri Maulana Malik Ibrahim Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.18860/jrce.v2i1.10333

Learning media is a useful tool and intermediary for facilitating the teaching and learning process to streamline communication between teachers and students. This community service activity is divided into three main activities, namely the delivery of concepts or theories of multimedia, types of multimedia, the use of multimedia, and making presentations using practical and interactive PowerPoints tools; second, training on how to use PowerPoint effectively; and third, evaluation on the ability of training participants in making multimedia-based teaching materials.

On the Forgotten Index and Jacobson Graphs Associated with Integer Rings Modulo n Jauhari, Mohammad Nafie; Jannah, Shahnaz Latifatul; Turmudi, Turmudi; Nisfulaila, Intan
KUBIK Vol 9 No 2 (2024): KUBIK: Jurnal Publikasi Ilmiah Matematika
Publisher : Jurusan Matematika, Fakultas Sains dan Teknologi, UIN Sunan Gunung Djati Bandung

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.15575/kubik.v9i2.39585

This paper investigates the connections between the Jacobson graph and the algebraic properties of rings through the analysis of the Jacobson graph of the ring \mathbb{Z}_{3p}, where p is a prime number greater than 3. The Jacobson graph of a commutative ring R is constructed by taking the elements of R, excluding its Jacobson Radical, as vertices, and connecting two distinct vertices if 1 minus their product is not a unit in R. The F-Index is utilized to capture and represent the structural properties of the ring through its associated graph. A detailed examination of the Jacobson Radical, maximal ideals, and vertex degrees in \mathbb{Z}_{3p} leads to the calculation of the F-Index, providing insights into the graphâ€™s connectivity and underlying algebraic structure. This study contributes to the intersection of algebra and graph theory, offering a foundation for further research into more complex algebraic structures.

On the Forgotten Index and Jacobson Graphs Associated with Integer Rings Modulo n Mohammad Nafie Jauhari; Shahnaz Latifatul Jannah; Turmudi Turmudi; Intan Nisfulaila
KUBIK Vol 9 No 2 (2024): KUBIK: Jurnal Publikasi Ilmiah Matematika
Publisher : Department of Mathematics, Faculty of Science and Technology, UIN Sunan Gunung Djati Bandung

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.15575/kubik.v9i2.39585

This paper investigates the connections between the Jacobson graph and the algebraic properties of rings through the analysis of the Jacobson graph of the ring \mathbb{Z}_{3p}, where p is a prime number greater than 3. The Jacobson graph of a commutative ring R is constructed by taking the elements of R, excluding its Jacobson Radical, as vertices, and connecting two distinct vertices if 1 minus their product is not a unit in R. The F-Index is utilized to capture and represent the structural properties of the ring through its associated graph. A detailed examination of the Jacobson Radical, maximal ideals, and vertex degrees in \mathbb{Z}_{3p} leads to the calculation of the F-Index, providing insights into the graphâ€™s connectivity and underlying algebraic structure. This study contributes to the intersection of algebra and graph theory, offering a foundation for further research into more complex algebraic structures.

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