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All Journal Kubik Prosiding SI MaNIs (Seminar Nasional Integrasi Matematika dan Nilai-Nilai Islami) Jurnal Matematika: MANTIK Jurnal Tadris Matematika KUBIK: Jurnal Publikasi Ilmiah Matematika Jurnal Riset Mahasiswa Matematika Jurnal Tadris Matematika Journal of Research on Community Engagement
Mohammad Nafie Jauhari
Universitas Islam Negeri Maulana Malik Ibrahim Malang, Indonesia
Arts Humanities Computer Science & IT Economics, Econometrics & Finance Education Mathematics Social Sciences

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Indeks Konektivitas Eksentrik Edis Pada Graf Annihilator dari Ring Bilangan Bulat Modulo Risma Amelia; Mohammad Nafie Jauhari; Erna Herawati
Jurnal Riset Mahasiswa Matematika Vol 4, No 3 (2025): Jurnal Riset Mahasiswa Matematika
Publisher : Universitas Islam Negeri Maulana Malik Ibrahim Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.18860/jrmm.v4i2.30059

Abstract

This study discusses how the general formula of the Ediz eccentric connectivity index (IKEE) in the annihilator graph of the ring of integers modulo. This study aims to determine the Ediz eccentric connectivity index on the annihilator graph of the ring of modular integers , with  is a primer number for , and  is a positif integer. The initial step in conducting this research is to form an annihilator graph from the ring of integers of the modul  , then find the vertex degree and the eccentricity of the vertex on the annihilator graph which is used to calculate the Ediz eccentric connectivity index of each graph. After that, formulate a conjecture about the Ediz eccentric connectivity index on the annihilator graph of the ring of integers of the modul  , and the last one proves the hypothesis obtained. The results of this study is general formula for the Ediz eccentric conductivity index on the Annihilator graph of the ring of integers modulo  where p is a prime number and m is a positive integer.
Pembobotan Ulang pada Graf Berbobot Negatif untuk Menerapkan Algoritma Dijkstra dalam Menentukan Lintasan Terpendek Natasya Thalia Salsabillah; Mohammad Nafie Jauhari; Achmad Nashichuddin
Jurnal Riset Mahasiswa Matematika Vol 5, No 1 (2025): Jurnal Riset Mahasiswa Matematika
Publisher : Universitas Islam Negeri Maulana Malik Ibrahim Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.18860/jrmm.v5i1.34383

Abstract

Algoritma Dijkstra merupakan algoritma untuk mencari lintasan terpendek yang bekerja secara optimal pada graf berbobot non-negatif. Namun, dalam berbagai permasalahan nyata seperti sistem transportasi dan jaringan keuangan, sering ditemukan sisi dengan bobot negatif yang menyebabkan Algoritma Dijkstra tidak dapat diterapkan secara langsung. Penelitian ini bertujuan untuk mengatasi keterbatasan tersebut dengan menerapkan metode pembobotan ulang menggunakan Algoritma Johnson. Metode ini mengombinasikan Algoritma Bellman-Ford dan Dijkstra untuk mengubah bobot negatif menjadi non-negatif tanpa mengubah struktur solusi optimal. Data yang digunakan berupa dua graf acak berarah yang masing-masing terdiri dari 31 simpul, yang dibuat menggunakan algoritma Erdos-Renyi. Hasil penelitian menunjukkan bahwa pembobotan ulang berhasil membuat bobot graf menjadi non-negatif sehingga Algoritma Dijkstra dapat diterapkan, dan hasil lintasan terpendek yang diperoleh sama dengan hasil dari Algoritma Bellman-Ford. Dengan demikian, metode pembobotan ulang menggunakan Algoritma Johnson terbukti efektif dalam menangani bobot negatif dan tetap menjaga keakuratan hasil pencarian lintasan terpendek menggunakan Algoritma Dijkstra.
Energi Detour pada Graf Invers dari Grup Quaternion Diperumum Iftitahur Rohmah; Mohammad Nafie Jauhari; Erna Herawati
Jurnal Riset Mahasiswa Matematika Vol 4, No 3 (2025): Jurnal Riset Mahasiswa Matematika
Publisher : Universitas Islam Negeri Maulana Malik Ibrahim Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.18860/jrmm.v4i2.30060

Abstract

A generalized quaternion group  is a non-abelian group with a  order constructed from the two elements  that is denoted by  defined as   where the  is the identity, . The inverse graph of a group is a graph which the vertices set are all elements of a finite group and two distinct vertices  and  are adjacent if and only if either  or . Graph energy, especially detour energy, is an important aspect in graph theory that describes network stability and resistance. The method used in this research is a qualitative method. This study aims to determine the formula of the detour energy in the inverse graph of the quaternion group is announced with . Through algebra analysis methods and graph theory, it is found that detour energy can be calculated using the detour matrix and the resulting eigen value. The results showed that the detour energy formula in the inverse graph from the quaternion group was founded was  for each .
Optimasi Algoritma Cheapest Insertion Heuristic dengan Algoritma Tabu Search dalam Pencarian Rute Terpendek Silviyatus Yulianti; Mohammad Nafie Jauhari; Achmad Nashichuddin
Jurnal Riset Mahasiswa Matematika Vol 4, No 6 (2025): Jurnal Riset Mahasiswa Matematika
Publisher : Universitas Islam Negeri Maulana Malik Ibrahim Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.18860/jrmm.v4i6.33343

Abstract

The shortest route finding problem is a significant topic in graph theory and combinatorial optimization, with wide applications in logistics, transportation, and scheduling. This research aims to improve the quality of the solution and time efficiency in solving the Traveling Salesman Problem (TSP) by optimizing the Cheapest Insertion Heuristic (CIH) algorithm using the application of the Tabu Search algorithm. The CIH algorithm constructs an initial solution by inserting points based on minimum weight. At the same time, the Tabu Search algorithm is applied to enhance the solution by avoiding local optima using a tabu list mechanism. The research data, consisting of the distances between parking retribution collection points by the Malang City Transportation Agency in Sukun Sub-district, were obtained from Google Maps. The algorithm performance evaluation is done by comparing the total mileage before and after optimization, and statistically analyzed using the Wilcoxon signed-rank test because the data does not follow a normal distribution. The results showed that optimizing the CIH algorithm using the Tabu Search algorithm significantly resulted in routes with shorter travel distances than using the CIH algorithm alone. This finding proves that optimizing the CIH algorithm with Tabu Search increases the effectiveness of finding the shortest route.The shortest route finding problem is a significant topic in graph theory and combinato-rial optimization, with wide applications in logistics, transportation, and scheduling. Thisresearch aims to improve the quality of the solution and time efficiency in solving the Trav-eling Salesman Problem (TSP) by optimizing the Cheapest Insertion Heuristic (CIH) algo-rithm using the application of the Tabu Search algorithm. The CIH algorithm constructs aninitial solution by inserting points based on minimum weight. At the same time, the TabuSearch algorithm is applied to enhance the solution by avoiding local optima using a tabulist mechanism. The research data, consisting of the distances between parking retributioncollection points by the Malang City Transportation Agency in Sukun Sub-district, were ob-tained from Google Maps. The algorithm performance evaluation is done by comparing thetotal mileage before and after optimization, and statistically analyzed using the Wilcoxonsigned-rank test because the data does not follow a normal distribution. The results showedthat optimizing the CIH algorithm using the Tabu Search algorithm significantly resulted inroutes with shorter travel distances than using the CIH algorithm alone. This finding provesthat optimizing the CIH algorithm with Tabu Search increases the effectiveness of findingthe shortest route.
Co-Authors Achmad Nashichuddin Anisatur Rizqiyah Annisa Hardiningsih HR Anwar, Nurul Hafidhoh Armeyntan, Tata Sutrafia Bella Nafa Savitri Dayanti, Vivi Dewi Ismiarti Elly Susanti Erna Herawati Evawati Alisah Fika Wahyuni Hairur Rahman Hairur Rahman Harini, Sri Hisyam Fahmi Iftitahur Rohmah Intan Nisfulaila Jannah, Shahnaz Latifatul Juhari Juhari, Juhari Lestari, Qhonita Guruh Dwi Lubab, Ahmad Mohammad Jamhuri Mufinnun, Nur Fatin Muhammad Khudzaifah Muhammad Khudzaifah Muhammad Khudzaifah Muhammad Khudzaifah Nasichuddin, Achmad Natasya Thalia Salsabillah Nisful Laila Novianti, Chofifah Alfin Nur Fatin Mufinnun Nurul Hafidhoh Anwar Reta, Tre Hayu Ria Risma Amelia Riyan Fahmi Syihabuddin Rizqiyah, Anisatur Safitri, Sukmawati Indah Salsabila, Wardatun Naura Savitri, Bella Nafa Shahnaz Latifatul Jannah Silviyatus Yulianti Sri Harini Susanti, Elly Syihabuddin, Riyan Fahmi Tre Hayu Ria Reta Turmudi Turmudi, Turmudi Wahyuni, Fika Wike, Wike Nur