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All Journal EIGEN MATHEMATICS JOURNAL Majalah Ilmiah Matematika dan Statistika (MIMS) Jurnal Pengabdian Inovasi Masyarakat Indonesia
Ghoffari, Lalu Hasan
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Indeks Padmakar-Ivan dan indeks Randic pada graf non-koprima dari grup bilangan bulat modulo Ghoffari, Lalu Hasan; Wardhana, I Gede Adhitya Wisnu; Abdurahim, Abdurahim
Majalah Ilmiah Matematika dan Statistika Vol. 24 No. 1 (2024): Majalah Ilmiah Matematika dan Statistika
Publisher : Jurusan Matematika FMIPA Universitas Jember

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.19184/mims.v24i1.45367

Abstract

Graph theory, introduced by the Swiss mathematician Leonhard Euler in 1736, has played a pivotal role in solving real-world problems since its inception, notably exemplified by Euler's solution to the Konigsberg Bridge problem. Its applications extend to various domains, including scheduling, shortest path routing, and chemical structure representation. In chemistry, graphs are extensively used to depict molecular structures and chemical compounds, aiding in visualizing atomic connections and overall compound configurations. Topology indices, such as the Padmakar-Ivan (PI) and Randic indices, provide numerical values capturing chemical bonding relationships. Beyond chemical structures, these indices find applications in abstract algebraic graph representations. Recent research, exemplified by Husni et al.'s work on the harmonic and Gutman indices, explores these indices in coprime graphs of integer groups modulo prime power orders. Additionally, studies on non-coprime graphs of integer groups modulo reveal unique characteristics and invariants, shedding light on their structure. The non-coprime graph is a graph with two vertices said to be adjacent if the greatest common divisor (GCD) of their orders is not equal to one. This paper aims to investigate the topological indices, specifically the Padmakar-Ivan and Randic indices, in non-coprime graphs of integer groups modulo, adding depth to our understanding of their applicability and significance in abstract algebraic representations. Keywords: Graph theory, padmakar-ivan index, randic index, non-coprime graphsMSC2020: 05C09
Hyper-Wiener and Szeged Indices of non-Coprime Graphs of Modulo Integer Groups Ghoffari, Lalu Hasan; Wardhana, I Gede Adhitya Wisnu; Dewi, Putu Kartika; Suparta, I Nengah
Eigen Mathematics Journal Vol 8 No 1 (2025): June
Publisher : University of Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.29303/emj.v8i1.244

Abstract

The non-coprime graph of the integer modulo group is a graph whose vertices represent the elements of the integer modulo group, excluding the identity element. Two distinct vertices are adjacent if and only if their orders are not relatively prime. This study explores two topological indices, the Hyper-Wiener index and the Szeged index, in the non-coprime graph of the integer modulo-n group. The results reveal that these indices are equal when the order is a prime power but differ when the order is the product of two distinct prime numbers. This research provides new insights into the patterns and characteristics of these indices, contributing to a broader understanding of the application of graph theory to abstract group structures.
Sosialisasi Penulisan Artikel Ilmiah untuk Pengganti Skripsi pada Mahasiswa Universitas Mataram Gayatri, Marena Rahayu; Ghoffari, Lalu Hasan; Husni, Muhammad Naoval; Febrilia, Baiq Rika Ayu; Syarifudin, Abdul Gazir; Putra, Lalu Riski Wirendra; Wardhana, I Gede Adhitya Wisnu
Jurnal Pengabdian Inovasi Masyarakat Indonesia Vol. 3 No. 1 (2024): Edisi Februari
Publisher : Program Studi Pendidikan Kimia FKIP Universitas Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.29303/jpimi.v3i1.3532

Abstract

Keputusan terbaru dari Kemendikbud Ristek yang menghapus persyaratan penulisan skripsi bagi mahasiswa merupakan sebuah terobosan penting dalam konteks pendidikan tinggi di Indonesia. Salah satu aspek utama dari kebijakan ini adalah penggantian skripsi dengan publikasi jurnal ilmiah. Sejalan dengan inisiatif ini, Program Studi Matematika Universitas Mataram telah menjalin kerja sama dengan Gamatika Research Club untuk mendistribusikan informasi terkait. Kegiatan sosialisasi ini melibatkan dua narasumber yang ahli di bidangnya. Narasumber pertama memberikan panduan lengkap mengenai prosedur dan pedoman untuk menggantikan skripsi dengan publikasi ilmiah, termasuk tahapan-tahapan yang harus diikuti oleh mahasiswa. Narasumber kedua memberikan tips, motivasi, dan wawasan mengenai pentingnya menerbitkan publikasi ilmiah bagi mahasiswa, serta menjelaskan manfaat dan peluang yang dapat diperoleh dari proses ini. Dengan demikian, kegiatan ini bertujuan untuk memberikan pemahaman yang komprehensif kepada mahasiswa mengenai perubahan ini dalam tata cara penyelesaian studi tingkat sarjana di lingkungan perguruan tinggi.
Co-Authors Abdul Gazir Syarifudin Abdurahim, Abdurahim Dewi, Putu Kartika Febrilia, Baiq Rika Ayu Gayatri, Marena Rahayu Husni, Muhammad Naoval I Gede Adhitya Wisnu Wardhana Prof. Dr.I Nengah Suparta,M.Si . Putra, Lalu Riski Wirendra