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All Journal BAREKENG: Jurnal Ilmu Matematika dan Terapan Basis : Jurnal Ilmiah Matematika
Syafitri, Hanna
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Computer Science & IT Control & Systems Engineering Economics, Econometrics & Finance Energy Engineering Mathematics Mechanical Engineering Physics Transportation

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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.
Indeks Harmonik, Hyper-Wiener, Dan Randic Dari Graf Pangkat Pada Grup Dihedral Syafitri, Hanna; Wardhana, I Gede Adhitya Wisnu; Abdurahim, Abdurahim; Alfian, Muhammad Rijal; Syechah, Bulqis Nebulla
Basis : Jurnal Ilmiah Matematika Vol. 4 No. 2 (2025): BASIS: Jurnal Ilmiah Matematika
Publisher : Universitas Mulawarman

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30872/xcf56e20

Abstract

Grup  disebut Grup Dihedral dengan order 2n, dinotasikan D2n, untuk bilangan asli n yang lebih besar dari 3 merupakan grup yang dibangun oleh dua element berbeda yaitu a dan b. Graf Pangkat dari grup dihedral D2n adalah graf yang semua simpulnya merupakan semua element dari D2n. Lebih jah, dua simpul berbeda, a dan b, dikatakan bertetangga jika dan hanya jika  ax = b atau by= a  dengan x dan y bilangan bulat positif. Pada artikel ini akan dikaji beberapa indeks topologi dari graf pangkat untuk grup dihedral, yaitu indeks Randic, Harmonik, dan Hyper-Wiener. Hasil penelitian ini berupa rumus umum dari indeks topologi dari graf pangkat grup dihedral.
Co-Authors Abdul Gazir Syarifudin Abdurahim, Abdurahim Husni, Muhammad Naoval I Gede Adhitya Wisnu Wardhana Muhammad Rijal Alfian Qurratul Aini Siboro, Ayes Malona