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All Journal BAREKENG: Jurnal Ilmu Matematika dan Terapan Square : Journal of Mathematics and Mathematics Education Journal of Fundamental Mathematics and Applications (JFMA)
Husni, Muhammad Naoval
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Computer Science & IT Control & Systems Engineering Decision Sciences, Operations Research & Management Economics, Econometrics & Finance Education Energy Engineering Mathematics Mechanical Engineering Physics Transportation

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THE CHEMICAL TOPOLOGICAL GRAPH ASSOCIATED WITH THE NILPOTENT GRAPH OF A MODULO RING OF PRIME POWER ORDER Malik, Deny Putra; Husni, Muhammad Naoval; Miftahurrahman, Miftahurrahman; Wardhana, I Gede Adhitya Wisnu; Semil @ Ismail, Ghazali
Journal of Fundamental Mathematics and Applications (JFMA) Vol 7, No 1 (2024)
Publisher : Diponegoro University

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.14710/jfma.v0i0.20269

Abstract

Chemical topological graph theory constitutes a subdomain within mathematical chemistry that leverages graph theory to model chemical molecules.  In this context, a chemical graph serves as a graphical representation of molecular structures. Specifically, a chemical molecule is portrayed as a graph wherein atoms are denoted as vertices, and the interatomic bonds are represented as edges within the graph. Various molecular properties are intricately linked to the topological indices of these molecular graphs. Notably, commonly employed indices encompass the Wiener Index, the Gutman Index, and the Zagreb Index.  This study is directed towards elucidating the numerical invariance and topological indices inherent to a nilpotent graph originating from a modulo integer ring with prime order. Consequently, the investigation seeks to discern how the Wiener Index, the Zagreb Index, and other characteristics of the nilpotent graph manifest within a ring of integers modulo prime order powers.
Ideal, Homomorfisma dan Gelanggang Faktor Pada Gelanggang Artin Satriawan, Didit; Husni, Muhammad Naoval
Square : Journal of Mathematics and Mathematics Education Vol 5, No 2 (2023)
Publisher : UIN Walisongo Semarang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.21580/square.2023.5.2.17610

Abstract

Pada penelitian ini akan ditunjukkan beberapa karakteristik dari gelanggang Artin seperti ideal prima, ideal maksimal, homomorfisma dan gelanggang faktor pada gelanggang artin. Hasil utama yang didapatkan dalam penelitian ini adalah jika R gelanggang Artin maka setiap ideal prima dari R adalah maksimal, kemudian jika R merupakan gelanggang Artin maka S juga merupakan gelanggang Artin, dan yang terakhir jika I dan R/I merupakan gelanggang Artin maka R merupakan gelanggang Artin
THE HARMONIC INDEX AND THE GUTMAN INDEX OF COPRIME GRAPH OF INTEGER GROUP MODULO WITH ORDER OF PRIME POWER Husni, Muhammad Naoval; Syafitri, Hanna; Siboro, Ayes Malona; Syarifudin, Abdul Gazir; Aini, Qurratul; Wardhana, I Gede Adhitya Wisnu
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 16 No 3 (2022): BAREKENG: Journal of Mathematics and Its Applications
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (354.985 KB) | DOI: 10.30598/barekengvol16iss3pp961-966

Abstract

In the field of mathematics, there are many branches of study, especially in graph theory, mathematically a graph is a pair of sets, which consists of a non-empty set whose members are called vertices and a set of distinct unordered pairs called edges. One example of a graph from a group is a coprime graph, where a coprime graph is defined as a graph whose vertices are members of a group and two vertices with different x and y are neighbors if only if (|x|,|y|)=1. In this study, the author discusses the Harmonic Index and Gutman Index of Coprime Graph of Integer Group Modulo n. The method used in this research is a literature review and analysis based on patterns formed from several case studies for the value of n. The results obtained from this study are the coprime graph of the group of integers modulo n has the harmonic index of and the Gutman index for where is prime and is a natural number.
Co-Authors I Gede Adhitya Wisnu Wardhana Malik, Deny Putra Miftahurrahman, Miftahurrahman Qurratul Aini Satriawan, Didit Semil @ Ismail, Ghazali Siboro, Ayes Malona Syafitri, Hanna